Farnsworth, who had spent the last few weeks as the team's primary closer, went 0-3 with a 3.18 earned run average and three saves over 19 games.
The 38-year-old right-hander took the loss against the Phillies on Sunday after giving up a run to break a 4-4 tie, but bounced back to post a save with a scoreless ninth against the Yankees on Monday.
"Disappointed," Farnsworth said when asked how he felt about the move. "It is what it is."
Farnsworth failed to make the Mets' Opening Day roster out of spring training, but was called upon after the team lost closer Bobby Parnell to an elbow injury in the first game of the season.