A number of countries including the US, Mauritius and Seychelles have already received the drug in the past few days while several others will get it by the weekend, they said.
Hydroxychloroquine has been identified by the US Food and Drug Administration as a possible treatment for the Covid-19 and it is being tested on more than 1,500 coronavirus patients in New York.
The demand for the drug has swelled rapidly in the last few days after India decided to lift a ban on its export.
In the neighbourhood, India is sending the drug to Afghanistan, Bhutan, Bangladesh Nepal, Maldives, Mauritius, Sri Lanka and Myanmar, sources said.
It is not immediately known whether Pakistan sought to procure the drug.
India is also sending hydroxychloroquine to
Zambia, Dominican Republic, Madagascar, Uganda, Burkina Faso, Niger, Mali Congo, Egypt, Armenia, Kazakhstan, Equador, Jamaica, Syria, Ukraine, Chad, Zimbabwe, France, Jordan, Kenya, Netherlands, Nigeria, Oman and Peru, the sources said.
They said it is being sent to the Philippines, Russia, Slovenia, South Africa, Sri Lanka, Tanzania, the United Arab Emirates, Uzbekistan, Urugway, Columbia, Algeria Bahamas, Mauritius and the United Kingdom.
The sources said the drug is being sent to several countries on a commercial basis while many others are getting it as India's grants.
In a recent telephonic conversation, US President Donald Trump requested Prime Minister Narendra Modi to allow the sale of hydroxychloroquine tablets ordered by the US to treat the growing number of coronavirus patients in his country.