There are two relevant differences between the "Top Conservative News" summary and the actual report from Swedish Radio, to which they are linking:
The Swedish Radio report does not mention the ethnicity of the perpetrator. Since the report refers to the number of police reports and not actual convictions, the perpetrator is likely to be unknown in several cases.
The Swedish Radio report only counts the number of reports in Stockholm County. The "Top Conservative News" summary seem to indicate that the numbers are for the whole country.
If we look at the statistics from "Brottsförebyggande rådet" (BRÅ), the actual number for the entire country are as expected quite a bit higher. In the first 7 months of 2013, there were in total 3,426 reports on rape or rape attempt. In 1,133 cases, the victim was below the age of 15 (1,004 girls and 129 boys).
The most recent statistics on crime among immigrants seem to be this report from BRÅ, dated 2005. The report does not quote any absolute numbers, but on page 42, the relative risk of being accused for different kind of crimes is listed for the three categories "born in Sweden, both parents born in Sweden", "born in Sweden, at least one parent born outside Sweden" and "born outside Sweden". For rape and rape attempts, the relative risks for these three categories are 1.0, 1.8 and 5.0.
Now, looking to find the percentage of the total population falling into each of these three groups, "Statistiska centralbyrån" offers the numbers for the year 2008:
- Born in Sweden, both parents born in Sweden: 75%
- Born in Sweden, at least one parent born abroad: 11%
- Born abroad: 14%
With the known risk of correlating three different statistics collected over a range of 8 years, the number of perpetrators in each of the three population groups (considering their share of the total population and relative crime risk) should be approximately:
- Born in Sweden, both parents born in Sweden: 1557
- Born in Sweden, at least one parent born abroad: 415
- Born abroad: 1454
Summing it up: Of the 3,426 reported rapes or rape attempts in the first 7 months of 2013, some 1900 can be assumed to have been performed by a perpetrator born outside Sweden or with at least one parent born outside Sweden.
This is where it seems impossible to get any further with the analysis. There are no public statistics regarding the religion of the foreign-born population and also no crime statistics with a more detailed breakdown of the nationality or religion of the crime suspects. Even if the Swedish Radio news report is misquoted and there are no further backups for the claim, it is not completely unrealistic, that 1000 of the assumed 1900 foreign rapists are Muslims.