Rand could not determine whether Ordonez's injury will heal in the minimum 15 days.
"That's hard to say," Rand said. "Right now we got to get it quiet and get the soreness out. Then we can start working strength and work our way back to baseball activity."
Ordonez underwent an examination by the team training staff Sunday morning at Comerica Park. He told reporters the pain increased overnight.
That makes three oblique injuries this month for the Tigers. Designated hitter Gary Sheffield just came off the disabled list after a left oblique pull, and utility man Brandon Inge went on the 15-day DL on Tuesday with a similar injury.
To fill Ordonez's roster spot, Detroit recalled outfielder Matt Joyce from Triple-A Toledo. Joyce makes his second stint with the Tigers this season. He played 18 games in May, batting .200 with five home runs and 10 RBIs. A fine defensive outfielder, Joyce has been one of Toledo's best power hitters over the last few weeks.
Last year's American League MVP runner-up and league batting champion, Ordonez has buoyed an inconsistent Detroit offense this season. He is hitting .307 with 12 home runs and 50 RBIs.
Scott McNeish is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.