Wyke missed Sunderland's 3-1 win over Plymouth Argyle with a thigh problem, while Johnson revealed that he will also need a minor operation on an infected tooth.
The latter is unlikely to affect his participation in the closing stages of the season, and Johnson hopes the former will prove not to be a major issue.
Aiden McGeady also missed the game with a swollen foot and a broken nose.
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However, the winger did travel with the squad to Home Park and so Johnson is hopeful that his injuries can be managed.
The win means that Sunderland's position ahead of the final game of the season against Northampton Town is much stronger ont that front, with a top-six place secured.
"We hope it's not serious but we'll have to see," Johnson said.
"It's a thigh problem, and we hope it's just a superficial tear rather than in the belly of the muscle.
"He's also got an infected tooth - well, bone really. That needs to be fixed and it'll be a little operation, but he should only be out for a couple of days."
Johnson also confirmed that the half-time withdrawal of Conor McLaughlin was pre-meditated.
McLaughlin has recovered from a hernia operation far more quickly than had been originally anticipated, and made his return at Home Park to allow Max Power to return to a midfield role.
McLaughlin was replaced by Carl Winchester at the break and Johnson said that was not due to any new concern.
Johnson wants to carefully manage his return to ensure he is as close to peak fitness as possible for the start of the play-offs.
"We felt it was the right risk to start him because with Conor we're chasing that play-off semi final.
"Although we needed to win today and he wasn't quite ready, we were chasing those 20 days to the semi.
"So it was always going to be 45 minutes for him and we thought it was better to start him and get the warm up etc. than throw him on after a couple of the jogs up the line or whatever."