Malaria affects more than 200 million people worldwide and killed an estimated 405,000 people in 2018 - most of them babies and children under five years old.
The United Nations AIDS agency and the WHO warned last week of stock shortages, with more than a third of the world's countries already saying they are at risk of running of antiretrovirals.
Several European governments moved on Wednesday to halt the use of the anti-malaria drug to treat COVID-19 patients, and a second global trial was suspended.
Fox News Channel, immediately after Trump's remarks, interviewed Dr. Bob Lahita, who cautioned people not to take hydroxychloroquine.
The vaccine - the world's first against malaria - will be administered to children under two and could be crucial to efforts to combat the disease, health officials said.