Trials in several countries are being "temporarily" suspended as a precaution, the agency said on Monday.
It comes after a recent medical study suggested the drug could increase the risk of patients dying from Covid-19.
President Donald Trump has said he is taking the drug to ward off the virus.
The US president has repeatedly promoted the anti-malarial drug, against medical advice and despite warnings from public health officials that it could cause heart problems.
Last week, a study in medical journal The Lancet said there were no benefits to treating coronavirus patients with hydroxychloroquine, and that taking it might even increase the number of deaths among those in hospital with the disease.
Hydroxychloroquine is safe for malaria, and conditions like lupus or arthritis, but no clinical trials have recommended its use for treating Covid-19.