General manager Billy King said Johnson is day to day and that he isn't worried about a long-term absence.
"If it were a playoff game, he'd probably push it," King said.
C.J. Watson started in Johnson's place Friday night.
Johnson suffered the injury Wednesday night in Milwaukee.
"It's better than it was two days ago," King said. "They've got him on medication and I expect him to be better tomorrow, and we'll see how it is Sunday [against the Memphis Grizzlies].
"If it's still tender and sore, we may keep him out, because it's a marathon we're trying to finish, not a sprint."
King later told reporters that Johnson would most likely be able to play Sunday night against the Grizzlies.
Johnson, 31, is averaging 17 points for the Nets (33-22) on 42.3 percent shooting. This will be the first game the veteran has missed this season.
King also said that interim coach P.J. Carlesimo will be evaluated at the end of the season, but it's fair to say that the job is his to lose.