The Knicks star used foul language and a gay slur Saturday while responding to a challenging Tweet posted by a fan using the Twitter handle @BFerrelli, Newsday reported.
The fan's message to Stoudemire read, "You better come back stronger and quicker to make up for last season" and included an obscenity at the end, the newspaper said.
The player responded with an offensive message that was sent privately but then "re-tweeted" publicly by the fan, the newspaper reported.
Stoudemire apologized in another Tweet made public by the fan, saying, "I apologize for what I said earlier. I just got off the plane and had time to think about it. Sorry bro. No Excuses. Won't happen again."
An NBA spokesman told Newsday in an e-mail Sunday he was certain the matter "will be reviewed" by the league.
The Knicks had no comment.
The exchange came as the NBA is running public service announcements in which the league in encouraging fans not to use gay slurs, the newspaper noted.