Right-handed reliever Jacob Rhame was optioned to Triple-A Las Vegas in a corresponding move.
Familia was placed on the DL June 8 with a sore right shoulder.
He has 14 saves in 18 opportunities this season and is 2-3 with a 2.48 ERA.
Familia was an All-Star in 2016 when he led all of Major League Baseball with 51 saves.
The Mets also got outfielder Jay Bruce back in their lineup Sunday after he had missed the team's past three games with a sore back. He was batting fifth and playing right field.