Melbourne football operations manager Ross Monaghan confirmed Johnson's injury on Tuesday.
"Paul's broken a small bone in his hand. He did that some time during the first half – he doesn't actually recall the incident – but there is clearly a break there and he needs to have some relatively minor surgery to correct it," he told melbournefc.com.au.
“He'll probably be out for three or four weeks at this stage, which is really disappointing for Paul because he's been in terrific form and he's been a really important player for us in the last couple of weeks and was having a real impact.
"It's disappointing for him, but we'll look forward to getting him back as soon as it's healed."
Monaghan praised Johnson's ability to play out the match with the injury.
"He was able to play out the game, but the doctors quickly identified that there was a problem there at half time," Monaghan said.
"Paul toughed it out in the second half and got through the game, which was a fantastic attribute from him.
“That'll give him a lot of confidence when he overcomes it and he'll be ready to get back into the play again."
Monaghan said it was an unfortunate setback for Johnson, considering his impressive form so far this year and the string of injury problems he had faced during his 30 AFL-game career since his debut in 2003.
"He's been showing really good form and I think the way we've been playing has really suited his style of play.
“In the first half [against Geelong] he took some big contested marks and was really running hard," Monaghan said.
"He's been handling it really well. He's been used to handling injuries and while he is disappointed, he is philosophical about the fact he is confident enough to know that he can come back in when he is fit and available.
"He'll give a good account himself as soon as he's ready to go."
