A person familiar with the situation told The Associated Press that Johnson
had a surgical procedure to repair a minor meniscus issue Tuesday and will not play in this weekend's East Regional games.
A spokesman said Johnson is expected to be able to play in the Final Four if Miami advances.
Miami (29-6) plays Marquette (25-8) on Thursday in the East Regional semifinals. The winner of that game will meet either Indiana or Syracuse for a trip to Atlanta and the Final Four.
In a statement, the university said Johnson was injured in last weekend's third-round game against Illinois. It was not immediately clear when Johnson was hurt in that game, and he was in the contest with 15 seconds remaining.
He played 18 minutes in all against the Illini, and Miami won the game 63-59.
Johnson has appeared in 26 games for Miami this season, starting nine. The 6-foot-10, 292-pound senior is averaging 6.7 points and 4.8 rebounds for Miami, and his presence could have been a major help against Marquette, which has outrebounded its opponents by 4.5 per game this season.
Marquette also has 31 offensive rebounds in this year's NCAA tournament, third-best in the field behind Michigan State (34) and Gonzaga (32).
Johnson has not been a regular starter for Miami since mid-December. He started three Atlantic Coast Conference games in early March, before returning to his reserve role at the start of the ACC tournament.
Information from The Associated Press was used in this report.