Berry, 28, was claimed by the Royals from Detroit in early June and outrighted to Triple-A Omaha. In 311 Triple-A at-bats this season between the Tigers' and Royals' organizations, he has hit .193 and has gone 28-for-32 in stolen-base attempts.
"We felt like we needed to have more of a pinch-runner at our disposal at some point in September and potentially beyond," Red Sox manager John Farrell said. "That's not to say he wouldn't get on the field in other ways, but more of a pure basestealer is the one area we felt we could upgrade."
The outfielder saw significant time down the stretch with Detroit last year, batting .258 in 94 games, with a perfect 21-for-21 steal rate.
Mortensen has appeared in 30 1/3 innings for the Red Sox this year, with a 5.34 ERA. The 28-year-old was optioned to Triple-A Pawtucket in late June and has a 2.47 ERA in 43 2/3 innings there. After being used solely as a reliever by Boston, he began starting games again in the Minors.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.