Johnson suffered ligament damage in the Dockers' round 10 loss to Richmond but bravely played out the match as several of his teammates succumbed to injury.
The 24-year-old was forced to go under the knife last week after struggling to shake off the complaint.
And in a further blow to the Dockers, youngster Brock O'Brien - who has played just three games since making his debut in 2007 - will miss the rest of the season with a quad injury.