Twins manager Ron Gardenhire said the 2006 MVP was day to day after he experienced dizziness during their 8-5 loss to the Rangers.
Morneau is hitting .298 with 28 home runs and an AL-best 94 RBIs. Brendan Harris, who started the game at shortstop, replaced Morneau at first.
Gardenhire also announced that left-handed pitcher Francisco Liriano will be placed on the disabled list before Tuesday's game because of a tired arm.
Liriano gave up seven runs, tying a career high, in two innings against the Rangers. Gardenhire said the Twins will call up Philip Humber from the minors.
"He's frustrated," Gardenhire said of Liriano. "He has no life on his pitches. We didn't want to take any chances."