The move is retroactive to April 21.
Grilli has not seen action since blowing saves in back-to-back games in last weekend's series against the Milwaukee Brewers.
Mark Melancon will take over as the team's closer until Grilli is healthy enough to pitch.
Grilli, 37, is 0-1 with a 4.50 ERA, four saves and seven strikeouts this season for the Pirates, who have lost three games in a row and are 2-8 in their last 10 games. CHEN: Pirates prospect Gregory Polanco is baseball's Next Big Thing