Bruce was placed on the paternity leave list Friday, with his wife due to give birth to the couple's second child. He was replaced on the 25-man roster by first baseman Dominic Smith, who was recalled from Triple-A Las Vegas.
The Mets also placed right-hander Hansel Robles on the 10-day disabled list, retroactive to Wednesday, with a sprained right knee.
Left-hander Buddy Baumann was recalled from Triple-A, but he'll have to sit out Friday night's game against the Phillies to serve a one-game suspension for his role in a brawl with Colorado on April 11. Baumann was pitching for San Diego then.