Mooney will miss the first ODI international against Pakistan in Clontarf next month, and the Leinster Lightning Inter-Provincial games against Northern Knights on May 6, and North West Warriors on May 14-16.
The 31 year-old was found to be in breach of clause eight of his Cricket Ireland contract which prohibits players from any public statements which it considers "denigrates, is derogatory, or is prejudicial to the interests of cricket; or is of a nature which brings the game of cricket or Cricket Ireland into disrepute."
Warren Deutrom, Cricket Ireland Chief Executive said: "John accepted that the tweet was offensive and inappropriate. We took into consideration the fact that he issued a fulsome and swift apology and that he is genuinely remorseful for his action. However given the breach of his contract and nature of the tweet, we felt it appropriate that a three match sanction be imposed. We have also severely reprimanded John and reminded him of his duties and responsibilities as a high profile international cricketer."
The player has accepted the Cricket Ireland decision and both he and Cricket Ireland consider the matter closed and will be making no further public comment on the issue.