Henn, 32, built a 3-5 record and 2.81 ERA across 52 appearances with the 51s. Over 57 2/3 innings, he had 49 strikeouts and 32 walks.
"I'm throwing the ball well," Henn said Friday. "I'm just glad somebody noticed and gave me an opportunity."
The Yankees selected Henn in the 2000 First-Year Player Draft. He pitched for them from 2005-07, followed by a year with San Diego and an '09 campaign that was split between Minnesota and Baltimore. In 60 Major League appearances, Henn is 2-9 with a 7.56 ERA.
Mets manager Terry Collins said every one of his left-handed relievers will likely pitch in this weekend's series, considering the Indians have 10 hitters capable of batting left-handed (four of whom are switch-hitters).
"It's definitely nice to be back," Henn said. "If this is my last hurrah, I'd rather it be in a Major League uniform than a Minor League uniform.
"It's definitely an opportunity, and I'm going to try to show these guys what I got."
Mark Emery is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.