The team now has seven players out of the lineup, the Milwaukee Journal Sentinel reported. Lucroy, who had a .388 batting average in May and an even higher .571 with runners in scoring position, is an especially difficult loss.
Lucroy told MLB.com he was hurt Sunday night in his hotel room. He said he was trying to retrieve a sock when his wife moved a suitcase that fell on his hand.
On Monday, he discovered he was unable to grip a bat properly.
Lucroy is expected to be out four to six weeks. George Kottaras, the team's backup catcher, is out with an injured hamstring, so the team called up Martin Maldonado.
"It's not going too well in that area," Manager Ron Roenicke said of Lucroy's injury. "Obviously, it hurts our team a lot. I feel really bad for him. And he feels really bad about it."