Johnson limped off before half-time after twisting awkwardly in a tackle. He was subbed during the break and returned to the bench on crutches.
Freo coach Ross Lyon confirmed the injury after the match and expects to be without his veteran defender for at least a fortnight.
Ross Lyon Post-Match Q & A
"He's got a slight medial, maybe a grade one, maybe a grade two," Lyon said.
"That's anywhere from two to four weeks. So he won't play in the near term."
The coach was pleased with his side's performance against the Crows, particularly after half-time. The Dockers trailed at the major change after butchering opportunities in the second quarter only to blow the game open with an emphatic display in the second half.
"I thought we dominated the second half," Lyon said.
"(I'm) probably a bit frustrated we kicked 12.18. I think it was 18 shots to six after half-time. Speaking to the group, they acknowledged it, and I thought it was a powerful response under some adversity with Johnson going down."
The Dockers kicked very poorly throughout the day but their set-shot conversion brought back memories of last year's Grand Final. They missed eight set-shots in the first half, which included two kicks out of bounds on the full.
Lyon said goalkicking was always a work in progress.
"We don't ignore it," Lyon said.
"There's no silver bullet.
"There was some set-shots, there was some snaps.
"We're mindful of it but we've just got to keep working on it."
The Dockers have won three games in a row and there is some external expectation that the winning streak could roll through the next seven matches and beyond.
Fremantle faces Richmond, the Brisbane Lions, West Coast, Melbourne, GWS, St Kilda and Carlton in the next seven rounds before travelling to Simonds Stadium to meet Geelong in round 20.
But Lyon hosed down any talk of what could potentially be achieved over the next two months.
"Odds and people's perceptions and supposed view of draws doesn't get it done," Lyon said.
"The only thing that gets it done in the AFL jungle is action and repeated action, whether it be training or a game.
"We have got plenty to improve on. We're still a fair way off really."
