The player, who has not been identified, was "immediately self-isolated," and contact tracing has started.
"All of the player's close contacts were identified and were informed to remain home today," said the statement. "Those individuals will participate in meetings remotely. We are working closely with the NFL's Chief Medical Officer regarding next protocol steps."
The Giants added that the rest of the team is continuing to follow its normal practice and meeting schedule.
MORE CORONAVIRUS COVID-19 COVERAGE
How coronavirus changed the New York region
Do you have coronavirus symptoms?
New York, New Jersey, Connecticut out-of-state travelers quarantine list
COVID-19 Help, Information. Stimulus and Business Updates
UPDATES
New York City
New Jersey
Long Island
Westchester and Hudson Valley
Connecticut
Centers for Disease Control and Prevention on coronavirus
Submit a News Tip