WASHINGTON—Navy leaders have relieved the captain of a U.S. aircraft carrier after a memo to military officials in which he pleaded for help with a coronavirus outbreak at sea was leaked to a newspaper.

Capt. Brett Crozier, the commanding officer of the USS Theodore Roosevelt, now at port in Guam, was relieved Thursday after superiors said they lost confidence in his ability to lead. The decision to remove him drew outrage from lawmakers and some relatives of crew members who backed the commander’s call for attention to the...