Ayanbadejo tore his left quadriceps in Sunday's game against New England. A three-time special teams Pro Bowler, Ayanbadejo has six special teams tackles this season.
He also ranks second on the Baltimore defense with 22 tackles.
Burgess was signed Tuesday off New England's practice squad. Drafted in the sixth round by the Ravens in 2007, he was traded to the Patriots on Sept. 22 for a conditional draft pick.