Dr. James Andrews ruled out surgery and said the 36-year-old Grilli should rest his arm for 10 to 14 days. A pitcher with such an injury typically is sidelined four to eight weeks, Pirates general manager Neal Huntington said.
The regular season ends in nine weeks, and the Pirates are in playoff contention.
Manager Clint Hurdle was pleased to learn about Grilli's prognosis.
"About as good as we could hope for," Hurdle said Friday before his team began a weekend series in Miami. "I'm happy for him, I'm happy for us. There's a chance we can get him back still with a lot of games left on the docket."
Grilli, who was tied for the National League lead with 30 saves, hurt his arm Monday against the Washington Nationals. Mark Melancon will continue to fill in for Grilli as the closer, and Hurdle said he probably won't designate a specific reliever for the seventh or eighth innings.
"It could be more of a committee setup," he said. "We're probably not going to pinpoint anybody."
Grilli was examined by team doctors and then received a second opinion from Andrews, who performed reconstructive elbow surgery on the right-hander 11 years ago.
Grilli, who has endured an injury-plagued career, entered the season with only five career saves but has thrived in the closer's role and made the All-Star team for the first time.