The right-hander has missed Boston's last two games. His last appearance came in Saturday's 2-1 win over Tampa Bay, during which he came out after facing just two batters in the ninth inning.
Hanrahan had been roughed up for five runs, including a pair of homers, in his previous appearance during an April 10 blown save and loss to Baltimore.
Andrew Bailey, who blew a save but ended up with a win Monday against Tampa Bay, will likely take over as Boston's primary closer until Hanrahan returns.
The Red Sox recalled pitcher Steven Wright from Class AAA Pawtucket to fill Hanrahan's roster spot.