The 32-year-old right-hander, who collapsed in the Chicago White Sox dugout on April 20 because of a ruptured aneurysm and brain hemorrhage, appeared in three spring training games.
Farquhar gave up six runs, four hits and five walks over two innings. He did have a hitless inning against the Philadelphia Phillies on Thursday in his second outing.
"I think he just needs to pitch," Yankees manager Aaron Boone said. "We saw enough that suggest he can get back to where he was. He just needs to go out and not be in a hurry to do it, because he's a lot closer than it may appear."
Farquhar signed a minor league deal with the Yankees during the offseason.