Naquin pulled up running into second base Friday night after his two-run double in the fourth inning against Kansas City. He was replaced in the top of the fifth and an MRI revealed the strain.
Naquin, primarily playing right field, is batting .333 with two homers and 11 RBI in 30 games.
Olson was placed on the paternity list Friday when Andrew Miller was activated after missing more than two weeks with a hamstring injury. Miller gave up a two-run homer to Salvador Perez in the seventh inning Friday and took the loss in a 9-8 defeat.
Olson is 0-1 with a 6.75 ERA in 15 appearances.