MLB.com reports Bartlett sustained the injury sliding into home plate during the sixth inning of Sunday's game against Cleveland.
Bartlett was hurt after replacing left fielder Josh Willingham, whose left wrist was hit by a pitch against Cleveland. According to the Associated Press, Willingham was out of the lineup for the Twins on Monday.
Right fielder Oswaldo Arcia was also out of the lineup for a third straight game because of a sore right wrist.
Herrmann played in two games for Rochester at the start of the year. He went 7-for-17 in 14 Spring Training games with the Twins. Last season he appeared in 57 games, batting .204 with four homers and 18 RBIs.
The Twins are playing in their home opener Monday afternoon against the Oakland Athletics.