Bay was chasing down a fly ball during Friday's game against Cincinnati at Citi Field when he crashed into the wall.
The concussion was the second such injury for Bay. He missed the second half of the 2010 season when he hit the wall at Dodger Stadium.
Bay spent time on the DL earlier this season when he fractured a rib. He was batting .187 with four home runs in 22 games this year.
The Mets took infielder Justin Turner off the 15-day disabled list Saturday to take Bay's spot on the roster.