Mateo was acquired last week from Oakland for a player to be named or cash, in the first trade since the transaction freeze was lifted.
Padres manager Jayce Tingler said Mateo has not been to the ballpark and is self-isolating.
San Diego announced last week that outfielder Tommy Pham tested positive for coronavirus and was asymptomatic. He has not yet rejoined the team.
The Associated Press contributed to this report.