As mentioned in the comments, the original source of this claim is K. S. Lal, Growth of Muslim Population in Medieval India (Delhi: Research Publications in Social Sciences, 1973).
He claims a population of 200 million in AD 1000, based on an analysis of Jatindra Mohamed Datta's article "Proportion of Muhammadans in India Through Centuries" (Modern Review, Calcutta, January 1948). Datta cites Firishta, a 17th century historian who supposedly gave the population for 1000 as 600 million, but Lal was unable to find this number in Firishta's text himself. Datta also uses W. H. Moreland's India at the Death of Akbar (London: Macmillan, 1920) as an outside estimate of something over 100 million. However, as one might guess, Datta chose the figure of 200 million not from a strict mathematical balance between Firishta and Moreland, but to represent a thesis he already believed:
[T]he population was very much greater [on the eve of Turkish
invasions] than at the death of Akbar. During centuries of invasions,
constant oppression and misrule, the wholesale massacres during the
Pathan period, the population of India dwindled ... This broad fact
emerged from the two estimates [Ferishtah's and Moreland's], however
erroneous or full of fallacies they may be. (Datta 1948 p. 32, quoted
in Lal 1973 p. 32)
Firishta's number, if indeed it was Firishta's and was not invented from whole cloth by Datta, was clearly off the top of his head. Both Lal and Datta admitted that Moreland's estimate is similarly speculative, and both quoted a demographer named Carl Saunders acknowledging this: "Moreland's figure has been quoted with favour in the census reports of India and no better estimate is available, but its factual basis is of the most slender kind." (Saunders, World Population, quoted in Datta, quoted in Lal p. 21).
Lal critiques two estimates found in Colin Clark, Population and Land Use (New York: Macmillan, 1967) and by Pran Nath, Study in the Economic Condition of Ancient India (London: Royal Asiatic Society, 1929) which give the population in AD 1000 as 70 million and 140 million, respectively. Lal does not like either estimate because both writers claim that the population was unchanged between 300 BC and AD 1000, which Lal considers ignorant of the effects of agricultural technology on sustainable population. (Lal, 26n, 28) However, Lal did like Nath's study enough to use his figure of 140 million for 300 BC as a starting point.
Another estimate by Colin McEvedy and Richard Jones, Atlas of World Population History (Penguin, 1978), gives 30 million in AD 1000. Maddison Angus, in the OECD report The World Economy: A Millennial Perspective (2001), gives 5 additional recent estimates for AD 1000 ranging from 40 to 77 million and comments, "India does not have statistical records of the same sort as Western Europe, China or Japan, and there is consequently a wide range of views."
The population of India according to Lal was 150 million in 1650, 172.5m in 1750, and 170m in 1800 (Lal, 201). These later estimates may be praiseworthy, as Wikipedia insinuates, but Lal's figure for AD 1000 is based almost entirely on his assumption that massacres caused millions of deaths, so writers who use the raw numbers as evidence for a massacre are committing the fallacy of circular logic. Estimates by writers quoted above range between 30 million and 600 million, which indicates a lack of certainty.
Lal does provide evidence of massacres in his book, but I am not an expert on medieval India so I will not investigate those claims here. Nothing in this source makes it totally evident to me that we know whether the population really did increase or decrease. In fact Lal admits that premodern primary sources such as Arab travelers are extremely unreliable with numbers.
