The team said McCutchen has been diagnosed with an "avulsion fracture involving the costochondral cartilage of the left 11th rib," and that it will continue to evaluate his progress.
"We want to take the appropriate time to make the best possible decision for Andrew," the Pirates said.
Costochondral cartilage is the junction of the rib (costo) and the cartilage (chondral). Avulsion means that instead of the muscle fibers tearing, the muscle pulled away from its attachment.
The Pittsburgh Post-Gazette reported Monday that McCutchen could be out three weeks or a month.
In the eighth inning of Sunday's game against the Arizona Diamondbacks, McCutchen hit a sacrifice fly and grabbed his left side as he jogged to first base. He needed help leaving the field and walking down the dugout steps.
Though he was hit in the back by a pitch on Saturday against the Diamondbacks, that has not been cited as the reason for McCutchen's present injury.
McCutchen said he couldn't be sure if getting hit caused the injury but that he has "taken a million swings and have never felt anything in my side until Sunday."
"I'm not going to play today and I'm not going to play tomorrow but we'll see after that," McCutchen added Tuesday. "Two days ago, I couldn't even bend down to put my shoes on. Now, I can ... get dressed like normal, so I'm getting better."
McCutchen has never been on the disabled list and has played in all but 25 games (843 of 868 games) since he entered the major leagues in June 2009, according to ESPN Stats & Information.
Pirates manager Clint Hurdle said the Pirates' medical staff is having difficulty putting a timetable on McCutchen's return because the injury is a rarity in baseball.
"They are trying to get as much information as they can," Hurdle said. "At this point we're weighing whether Andrew might be able to come back in less than 15 days against playing a man short. For now, we're going to wait and keep him on the active roster."
The loss of McCutchen would be a major blow to the Pirates, who sit 1½ games behind the first-place Milwaukee Brewers in the National League Central and are a half-game back of the second wild-card slot. McCutchen is hitting .311 with 17 home runs and 67 RBIs this season.
Also Tuesday, the Pirates recalled outfielder Starling Marte from his rehab assignment and reinstated him from the seven-day concussion DL.
Marte, sidelined since July 21, went 1-for-12 in three games with Triple-A Indianapolis, playing two games in left field and one in center field.
To make room on the active roster, Pedro Alvarez has been placed on the bereavement list.
Information from ESPN's Stephania Bell and The Associated Press is included in this report.
McCutchen Could Miss A Month
The Baseball Tonight crew breaks down the impact Andrew McCutchen's absence will have on the Pirates.