Grace initially injured the elbow on July 28, then aggravated the injury in Arizona's 8-5 win over Montreal on Tuesday.
In 57 games this season, the 39-year-old Grace is batting .195 with three homers and 16 RBI. His last homer came May 25.
The Diamondbacks have other injury problems. Outfielder Steve Finley, who injured his shoulder in a collision with Junior Spivey on Tuesday, was scratched from the starting lineup Wednesday and is listed as day-to-day.
To fill Grace's roster spot, the Diamondbacks recalled infielder Robby Hammock from Triple-A Tucson. Hammock played 33 games for the Diamondbacks earlier this season, batting .274 with five homers and 18 RBI.
Celebrity Families of 2014 [PHOTOS]