In direct reply to the question, the study on which the comment seems to be based looked at children in Rumanian orphanages and does not provide any evidence to support the claim.
But: The concern is not completely made up and there seems to be some debate in scientific literature whether early childcare may be correlated with (very slightly) reduced cognitive performance later in life. Some studies have found correlations between early childcare and reduced performance in tests measuring some form of cognitive capacities in preschoolers (Bracken School Readiness Test) but they do not show (nor claim) a causal link. Other studies disagree and do not find any such correlation. There seems to be agreement that bad quality care (from childcare or parents) will negatively affect a child's development, which is probably not surprising.
It seems that there are indeed several scientifically credible studies that found a small correlation between early childcare (starting 6 to 9 months, not 2 years as stated in the Blick article) and lower scores on the Bracken test for school readiness. While this test is not an IQ test (as far as I understand) and does not measure intelligence, it is a measure of cognitive capacity. Most studies that I found were based on the National Institute of Child Health and Human Development Study of Early Child Care (NICHD-SECC) which is an US based data set.
An article in Child Development by Waldfogel et al.
in 2002 seems to be one of the most prominent in this direction. Note that the journal is scored Q1 in various related areas by Scimago so I assume it is a credible scientific source. The article itself has been cited over 700 times, so it has clearly received lots of attention from the scientific community. In their literature review they conclude
The studies that have examined the effects of first-year maternal employment separately from the effects of employment later in the preschool years have tended to find negative effects of first-year maternal employment on children’s later cognitive outcomes
Generally, most studies equate maternal employment with childcare which is probably not 100% accurate but the overlap is likely very large and I found this methodology in various papers, so it seems undisputed.
Waldfogel's own analysis confirms the correlation. They conclude
Taken together, the results of the present study illustrate the extent to which the effects of early maternal employment on children’s cognitive outcomes depend crucially on both the quality of care that children receive at home and the quality of care that children receive in child care. Good-quality care at home, and good-quality child care, can go a long way toward buffering the negative links between early maternal employment and later child outcomes. Nevertheless, it is concerning that even after controlling for home-environment quality and child-care quality, full-time maternal employment by the ninth month was found to be associated with lower Bracken scores at 36 months. Until there is better understanding with regard to what causes this association and how to buffer it, it would be prudent for policy makers to go slow on measures (such as the recent Temporary Assistance to Needy Families reforms) that would require mothers to enter the labor force (full-time) early in the first year of life and to consider measures (such as proposed FMLA extensions) that would allow more mothers to choose to delay their return to the labor force and/or to work part-time until later in
the first year of life.
So based on a US data set, tracking a cohort of children born in 1991, there is some evidence of a correlation between early childcare and slightly lower cognitive capabilities later in life.
However, there are more recent studies that question those findings, e.g. by Lombardi and Coley in 2017. They provide a comprehensive overview of related work and conclude
A sizable body of empirical evidence using large, longitudinal survey studies of U.S. children has generated conflicting findings about the implications of maternal employment in the first 2 years after childbirth for children’s long-term development.
For example, assessing a sample of White children from the NICHD-SECC, Brooks-Gunn et al. (2002) found that maternal employment begun before the child’s 9th month was linked to lower child cognitive skills at 36 months. This pattern continued into the first grade, extending to children’s behavioral functioning as well (Brooks-Gunn et al., 2010). Research with a nationally representative sample of mothers, the NLSY-CS, has unearthed similar patterns (Han et al., 2001; Hill et al., 2005). In contrast, at least one study using a more contemporary nationally representative sample of children born in 2001 found no links between maternal employment begun by 9 months or 24 months after childbirth and children’s cognitive and behavioral skills in kindergarten (Lombardi & Coley, 2014).
So it seems that 15 years after the Waldvogel study, no consensus and in particular no convincing causal link has emerged. Furthermore, in their study, Lombardi and Coley fail to find any correlation for children in the UK and Australia:
In the context of these cautions, findings from the present study suggest that early movements into employment following childbirth may not be associated with developmental risks or benefits for most modern children in Australia and the United Kingdom. These results were replicated across multiple statistical models in contemporary birth cohort studies in these two countries.
These findings are good news - maternal employment is a norm worldwide and an important contributor to both families’ and countries’ economies. As seen in the descriptive findings from this study, the majority of mothers in the United Kingdom (nearly 60%) returned to work within the first 2 years after childbirth, whereas a smaller percentage, more than one third, of Australian mothers were working by the time their child was 2 years old. Families and societies benefit from mothers’ work: It supports women’s careers, encourages balanced gender roles, and increases families’ economic resources (Gornick & Meyers, 2003; Waldfogel, 2010). Our findings suggested that children from Australia and the United Kingdom are not harmed by this employment.
Note that his in particular contradicts the statement in the Blick article which claimed that childcare was especially harmful to children below 2 years of age.
Therefore, the correlations found earlier by Waldfogel could be chance results or may be only valid for the specific situation in the US and/or the 1991 cohort of children they studied (since a study of children born in the 2000's could not replicate their findings).
In summary, at least from these two papers and from the way they summarize the relevant literature, there does not seem to be much evidence of a causal link between childcare and lower cognitive capacities. In particular, I see no evidence whatsoever for the rather sensational claim in the Blick article that "Every additional month that children spend in the day care center means that they have a reduced IQ later between the ages of 8 and 14".