The three-time All Australian, who was already unavailable for the Cats' round one clash with Hawthorn due to suspension, had been suffering knee soreness for a week.
"Stevie's had a few injuries in his career that he has miraculously recovered from … but he's had a little grumble with his knee," Geelong physio Mike Snelling told CatsTV.
"He's had a very small scope, which was very successful.
"This will only be a few weeks and then we'll see Stevie back."
The Cats say they are taking a long-term approach with Johnson.
"There was a possibility that Steve could manage the issue through the season," Geelong football manager Neil Balme added.
"But we all felt it was a better course of action to have the procedure now so that Steve will be at 100 per cent when he returns.
"We think that by having the knee cleaned up he will be fully fit when he starts to play, rather than the possibility that the knee will slowly deteriorate over time forcing the surgery later in the year."
Emerging defender Cameron Guthrie is another player certain to miss the Easter Monday blockbuster against the Hawks after suffering a calf tear in the warm-up prior to the practice match against Collingwood.
The Cats have also revealed that luckless midfielder Josh Cowan recently travelled to London where he had surgery on his troublesome Achilles.
"We sought an opinion overseas from a world expert and it was very successful," Snelling said.
"He had a little muscle problem near his Achilles that we've addressed.
"From the minute that he came out of surgery he felt much better, which is a real positive, and he's got a big smile on his face.
"His rehab's going to take a few weeks obviously, but we anticipate that we'll see him playing a fair bit this year.
Geelong promoted two rookie-listed ruckmen, Mark Blicavs and Josh Walker, to its senior list on Tuesday.
But the Cats continue to insist that fellow big man Trent West, who had knee surgery a month ago, is a genuine chance to play against the Hawks.
West has trained strongly during the past week.
"His rehab has gone really, really well, and he's probable for the weekend," Snelling said.
Steve Johnson is a midfielder/forward in NAB AFL Fantasy. He averaged 97.38 points in 2012. Register your team at our AFL Fantasy Hub.
Adam McNicol covers Geelong news for AFL.com.au. Follow him on Twitter at @AFL_AdamMcNicol
