India is a large producer of Hydroxychloroquine because, prior to the promotion of the drug as a potential treatment for COVID-19, its most widespread use was as an anti-malarial drug. India has, according to the WHO's World malaria report 2019, the largest proportion of malaria cases outside of Africa:
Nineteen countries in sub-Saharan Africa and India carried almost
85% of the global malaria burden.
The report also notes that India is the only one of the "high burden to high impact" countries (basically countries most affected by malaria) to have significant domestic investment into dealing with the disease compared to the reliance on international aid. This has manifested itself in the form of pharmaceutical manufacturers which can supply India with its domestic demand for the drug, such as Zydus Cadila and Ipca Laboratories.
This Forbes article notes that these companies in particular have significant capacity to ramp up production:
“The priority is to manufacture this drug versus anything else,” says
Sharvil Patel, managing director at Ahmedabad-based Zydus Cadila,
which had $1.9 billion in revenues in fiscal 2019. “We have ramped up
our production of hydroxychloroquine from 3 metric tons per month to
20 to 30 metric tons per month and can scale it up further to 40 to 50
metric tons if there is a requirement.”
Ipca Labs, which has 20-metric-ton capacity, can produce 100 million
tablets a month. “The Indian government has placed a significant
order,” says Ajit Kumar Jain, joint managing director of Ipca Labs.
“We can increase our manufacturing capacity to 26 metric tons in a
month or two. We are also simultaneously ramping up our packing and
labelling lines.”
[...]
Sudarshan Jain, secretary general of the Indian Pharmaceutical
Alliance, an industry group, says that “the domestic demand is 3
million tablets a month but we have the capacity to go up to 150
million to 200 million tablets a month easily.” He adds that “it is
very difficult to predict demand going forward because we do not know
how many will be affected.”
This is, of course, on top of the underlying fact that India is, according to Raconteur, the largest provider of generic drugs globally, with its pharmaceutical industry is growing by 7 to 8 per cent a year, with growth of 11 to 13 percent expected in 2020.
It seems that India's prominence in the manufacture of the drug is due to existing infrastructure due to high existing domestic demand, and a strong underlying pharmaceutical industry, giving it the ability to quickly scale up production levels.