Brewers manager Craig Counsell reiterated that hope, saying Braun could return to the lineup as early as Saturday.
Minor injuries have presented challenges all season for Braun, who has started 82 of the Brewers' 101 games in left field, plus one start as the designated hitter. Braun and the Brewers anticipated him occasionally missing games, since Braun had surgery in October for a bulging disk in his back.
He's missed time with oblique injuries in the past, including a DL stint in 2014 for a strained muscle on his right side.
"It's not fun, and obviously that's what we're trying to avoid," Braun said. "I felt it for a few days, but [Thursday] it just wouldn't loosen up so obviously it made sense to not take the chance to do something worse to it."
Braun's bat has cooled considerably of late; he is hitting .307 in July, but 20 of his 23 hits were singles.
Still, the Brewers received at least one trade offer for Braun, according to MLB Network's Jon Heyman, who reported Milwaukee officials considered the offer "terrible."
Adam McCalvy has covered the Brewers for MLB.com since 2001. Follow him on Twitter @AdamMcCalvy, like him on Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.