The move came just before the series finale against Houston, when newly acquired right-hander Hector Noesi was added to the Rangers' roster.
Beltre hasn't played since coming out of Tuesday's game at Boston. His DL move is retroactive to Wednesday, and he could be eligible to come off the DL as early as April 24, a day off for Texas.
The Tampa Bay Rays put right-hander Alex Cobb on the 15-day DL because of a strained muscle on his left side, the second starter they have lost to injury in a week.
Cobb pitched seven innings in a 1-0 win over the Cincinnati Reds on Saturday. He has pitched 15-1-3 innings without giving up a run.
The Rays called up left-handed reliever Jeff Beliveau from triple-A Durham (N.C.) to take his spot on the roster.
Left-hander Erik Bedard was added to the roster Sunday and will take Cobb's spot in the rotation for now.