Johnson went under the knife following the FA Cup second round loss to Chester in December, but is on course to return to training by the end of the season.
He said: "Hopefully I will be in position to play again six weeks after I start running and I hope to be able to do that within the next week or so.
"We haven't pencilled a date in as to when I might play again, all I'm bothered about is being fit for the start of next season."