The Rangers made the roster move Thursday after Moreland flew from Boston to Arlington, Texas, to undergo an MRI.
Moreland, who was examined by team physician Dr. Keith Meister, has a Grade 1 hamstring strain. He will remain in Texas and undergo treatment for the remainder of the Rangers' current road trip, which includes Thursday's game at Boston and a weekend series in Toronto.
Moreland, who is hitting .288 with 12 home runs and 29 RBIs, suffered the injury while running out a double during the Rangers' 3-2 victory on Wednesday night against the Red Sox. He slowed down between first and second base.
Rangers manager Ron Washington said after Wednesday's game that Jeff Baker will start at first base Thursday against the Red Sox.
Washington also said Lance Berkman will fill in at first base.
To replace Moreland on the active roster, the Rangers have purchased the contract of first baseman Chris McGuiness from Triple-A Round Rock. He is expected to arrive in Boston on Thursday night.
McGuiness, who will make his major league debut, is batting .275 with six home runs and 34 RBIs. He has a .382 on base-percentage.
The Rangers' other first base options in the minor leagues include Mike Olt, who homered on Tuesday and appears to be bouncing back from vision issues that sidelined him for a month starting on April 25.
The Rangers acquired McGuiness in a trade that sent Jarrod Saltalamacchia to the Red Sox on July 31, 2010. Cleveland picked him in the Rule 5 draft on Dec. 6, 2012, and McGuiness spent most of this spring training with the Indians before he was returned to the Rangers on March 27.