Cabrera left the Tigers' 6-4 loss to the Minnesota Twins in the bottom of the third inning Tuesday night with what the team initially said was a left biceps tendon strain. An MRI determined it was ruptured.
Cabrera, 35, will have season-ending surgery later this week.
"He feels bad, he feels really bad," Gardenhire said. "He feels like he's letting people down."
Cabrera suffered the injury when he swung awkwardly at Jake Odorizzi's slider. He immediately walked toward the Tigers' dugout with his left arm hanging at his side. When he was joined by team trainers, Cabrera gestured to his biceps and continued walking into the Detroit clubhouse.
Niko Goodrum replaced him at the plate and struck out.
"At the end of that inning, I ran up to check on him in the clubhouse, and he said he felt a pop on that swing," teammate Nicholas Castellanos said. "I knew that wasn't good, but we didn't find out how bad it was until after the game."
Many of the Tigers had already left the clubhouse before it was opened to the media, more than 20 minutes after the final pitch.
"We're all kind of stunned," Tigers outfielder JaCoby Jones said. "You don't think anything like that is going to happen to Miguel Cabrera, especially on a swing."
Cabrera has played through numerous lower-body injuries in the past few years, even while winning a Triple Crown, two MVP awards and four batting titles, but it started to catch up with him in 2017. He played 130 games, but hit a career-worst .249 with 16 homers.
This year, he missed three games with spasms in the same biceps tendon that ruptured Tuesday, then was out for 26 games with a hamstring strain and back tightness. He returned on June 1, hitting .244 with no home runs and one RBI in 12 games before the latest injury.
Gardenhire didn't think the earlier injuries played a role in what happened on Tuesday.
"He took BP before the game, and he said he felt great," Gardenhire said.
Cabrera was coming off the worst season of his career, hitting .249 with 16 homers as the Tigers went 64-98 in 2017.
But Cabrera was hitting .301 this season with three homers and 22 RBIs. He appeared in 38 games in 2018; the last time Cabrera played fewer than 100 games in a season was his rookie campaign in 2003, when he made his debut in June.
Between 2003, when he entered the majors, and 2016, Cabrera was placed on the disabled list once. Tuesday's injury will send him to the disabled list for the second time this season, and the fourth time in his career.
Cabrera's 2018 salary is $30 million, and he is due at least $162 million guaranteed on his contract after this season.
The slugger is chasing 500 career home runs and 3,000 career hits, an exclusive MLB club that comprises Hank Aaron, Albert Pujols, Willie Mays, Alex Rodriguez, Rafael Palmeiro and Eddie Murray.
Cabrera also ranks in the top three among all active players in hits, home runs and RBIs: His 2,676 hits are third-most, his 465 home runs are second-most and his 1,635 RBIs are third-most.
The Associated Press contributed to this report.