The Mets lost to the Cleveland Guardians on Monday night, 3-1, despite solid pitching as their offense went silent.
The Chicago Cubs have made a series of roster moves on their off-day, including activating shortstop Dansby Swanson from the 10-day injured list.
Rays manager Kevin Cash said the goal is for Eflin to be back in two to four weeks.
After a strikeout in the fourth inning, Mets right fielder Starling Marte was ejected by home plate umpire Manny Gonzalez on Monday night against the Cleveland Guardians.