Rose has a Grade 2 sprain of his left ankle but is still expected to start Game 2 of the Bulls' semifinal series against Atlanta Wednesday, CSN Chicago reported.
Rose twisted his left ankle in the final seconds of the Bulls' 103-95 loss Monday when he stepped on the back of Jamal Crawford's foot.
The MVP award was announced at a news conference in suburban Chicago.
Rose sparked the Bulls to the NBA's best record this season, averaging 25 points and 7.7 assists per game.
A group of 120 sportswriters and broadcasters that served as an election panel gave Rose a total of 1,182 points (including 113 first-place votes).
Also factored into the voting were fan ballots.
Finishing second was Orlando's Dwight Howard with 643 points and three first-place votes. He was followed by LeBron James of the Miami Heat (522 points, four first-place votes), Kobe Bryant of the Los Angeles Lakers (428, one first-place vote) and Kevin Durant of Oklahoma City (190 points).
"We're all excited because of not only how good he is on the court but he's a great kid," Bulls teammate Luol Deng told the Chicago Tribune. "He deserves it. What he did this year and the effort he put into it is unbelievable."