Votto is not expected to need surgery but could miss up to a month.
Kyle Farmer is among the options at first.
"We'll figure it out,'' manager David Bell said.
Votto was hit by a Dallas Keuchel pitch in the fourth inning. He remained in the game, but in the sixth was replaced at first base by Farmer.
"I knew I was in pain," Votto said after the game, according to MLB.com. "I thought I was being a baby. I just wanted to stay in the game, but I didn't think I could grip the bat and I was having a hard time putting my glove on. I could run and I was moving well, and I thought, 'Just give it some time, it should shake at some point. Maybe it's just one of those [where] your thumb gets jammed in a door or something like that and it just goes away.' It broke, what are you going to do?"
Keuchel expressed regret.
"It's a joy to pitch against him,'' Keuchel said. "You never want that to happen. I wish him well.''
Votto is hitting .226 with five home runs and 17 RBIs.
Information from The Associated Press was used in this report.