The Marlins don't feel Bonifacio will need surgery, but he could miss about a week. If that's the case, the team may decide to place him on the disabled list, just to give the injury more time to heal.
On Monday, Bonifacio will be examined by Marlins physicians in Miami.
"Our doctors have to check on him," Guillen said. "He's not going to play the next couple of days. We're in the process right now of what we're going to do."
The injury occurred while Bonifacio was attempting to steal second base. On the play, he was thrown out by Indians catcher Carlos Santana.
Bonifacio had stolen 20 consecutive bags to open the season before being tossed out. Dating back to last year, the center fielder had swiped 21 consecutive bases, which is a Marlins record.
On the play, Bonifacio's left thumb jammed into second base. The momentum of the slide carried him past the bag.
When he was unable to grip the bat on Friday night, he was removed from the lineup. Bryan Petersen got the start in center field on Saturday.
"I feel a little better," Bonifacio said early Saturday afternoon.
Bonifacio's 20 steals are the tops in the big leagues.
If Bonifacio goes on the disabled list, Chris Coghlan is likely to be recalled from Triple-A New Orleans. Kevin Mattison, regarded as the best defensive center fielder in the organization, could be another choice. But Coghlan has more MLB experience, and he can play both left field and center field.
"Everybody has to step it up until he comes back," Guillen said. "That's what good ballclubs do. Good ballclubs step it up and try to fill the hole. Whoever is going to replace him, just be who they can be, don't be Boni. Just play your game."
He said on Saturday that he had a little more mobility in his left hand than there was the night before. However, there is some swelling he is dealing with.
Bonifacio slides head-first, and he said that is the first time he's ever jammed his thumb on a base.
Guillen cautions that players risk injury when sliding head-first.
"I love it, but it's very dangerous," Guillen said. "You put yourself in position to get hurt. Every time you go down, you have a chance to be hurt. It could be shoulders, elbows, arms, fingers, wrists. But, that's instinct. That's the way baseball players are. I wish people slide feet first, but baseball instincts are baseball instincts."
Bonifacio's streak of 112 consecutive games was the third most in the National League. Heading into Saturday, Joey Votto topped the list with 165 games, and Michael Bourn followed with 129.