The all rounder said he hoped the former British Prime Minister's death was "slow and painful".
As punishment he'll miss the one day international with Pakistan on May 23rd in Clontarf and Cricket Ireland have "severely reprimanded" the 31 year old also banning him for two Irish Inter-Provincial matches.
He'll miss the Leinster Lightning games against Northern Knights on May 6, and North West Warriors on May 14-16.
Mooney will however be eligible for the second game against Pakistan on May 26th.
Mooney was quick to apologise for his tweets, admitting that they had been "offensive", but he was found to be in breach of clause eight of his Cricket Ireland contract.
It prohibits players from publicly stating anything which "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."
Mooney has accepted the decision by Cricket Ireland and both have said they will be making no further public comment on the issue.