The move was made retroactive to Sunday.
"Liriano said his hamstring was sore after his last start, and it hasn't gotten any better," manager Ron Gardenhire said Tuesday. "He's had a history of leg problems, but he is usually able to get through them. This time he couldn't."
Liriano is 3-2 with a 3.90 ERA in 10 starts this season.
The Tigers also placed left-handed reliever Daniel Stumpf on the 10-day DL with ulnar nerve irritation. That move was made retroactive to Tuesday.
"We're going through a tough stretch," Gardenhire said. "We're finally getting some guys healthy, and then we lose two."
Barbato has a 7.36 ERA in three appearances for the Tigers this season but was pitching to a 1.72 ERA in 12 Triple-A appearances. Carpenter is 0-1 with an 8.31 ERA in three appearances (two starts) for the Tigers this season. He is 1-5 with a 5.72 ERA in nine Triple-A starts.