The Mets were trying Thursday night for a four-game sweep against the Marlins before returning home Friday to face the Yankees in a three-game series at CitiField.
They now will focus on "additional coronavirus testing and contact tracing," MLB said in postponing the games.
Two members of the organization who tested positive were a player and staff member, both unidentified.
The Bronx Bombers were reeling after losing their third straight home game to the Tampa Bay Rays on Thursday, while the Mets looked for a four-game sweep Thursday night against the Marlins.
Click here to follow Daily Voice Rutherford and receive free news updates.