Villar was injured in the eighth inning of Friday night's 8-6 victory over Arizona when he made a diving stop of Chris Herrmann's grounder and threw the runner out.
Villar had to be carted off the field. Manager Craig Counsell said X-rays were negative.
Milwaukee recalled outfielder Lewis Brinson from Triple-A Colorado Springs to take Villar's roster spot.
Versatile Eric Sogard started at second for Milwaukee on Saturday night.
The Brewers already were without third baseman Travis Shaw and outfielder Ryan Braun. Shaw is on family medical emergency leave due to health concerns of his baby daughter, born earlier in the week. Braun has been on the DL since May 26 with a left calf strain.