Kelley, who was traded to the A's by the Washington Nationals last month, said he nearly cut the tip off his thumb when washing a sharp knife last Friday.
"A really sharp knife, too," he told the San Francisco Chronicle. "It went pretty deep. You know how usually when you cut your finger, it takes a second to start bleeding? This was instant. There was blood everywhere. It wasn't a fun afternoon."
Kelley said his fingernail kept the knife from completely severing the top of his thumb, where he releases the ball when he pitches.
"This is why you shouldn't wash dishes," he said jokingly, according to the Chronicle.
Kelley, 34, hasn't allowed a run in 10 appearances with the A's since the trade. He has struck out nine while allowing two hits and two walks in 8 2/3 innings pitched.
He said he expects to be able to return to the mound on Friday for the A's, who are second in the American League West and currently hold one of the two AL wild-card spots.