Narveson was working on his glove in the trainer's room Tuesday when he sliced his thumb and needed eight stitches to close the wound.
So far this season, Narveson has logged an 8-6 record with a 4.49 ERA in 23 starts for the NL Central Division leaders. He's 2-0 over his last four starts.
The Brewers recalled pitcher Frankie De La Cruz from Triple-A Nashville. The 27-year-old right-hander is 7-6 with a 3.88 ERA in 25 games (23 starts) for the Sounds this season.