States across the U.S. are taking steps to prevent hoarding of decades-old antimalarial drugs for treatment of the new coronavirus, an effort to preserve supplies for other patients who rely on the medicines to remedy ailments such as lupus and arthritis.

At least 20 states late last month began implementing emergency restrictions or guidelines to ease pressure on the supply of hydroxychloroquine and chloroquine for the autoimmune patients. Some states are limiting prescription sizes or asking pharmacists to make sure a patient...