Bairstow was expected to be available for the Stars after Christmas after completing the 14-day mandatory quarantine in Australia following England's limited-overs tour of South Africa. However, he is expected to be recalled to England's Test squad for the tour of Sri Lanka in January.
The Stars moved swiftly to sign Fletcher, who like fellow Stars signing Nicholas Pooran, has been in New Zealand playing in the T20I series.
"We're naturally disappointed Jonny won't be able to link up with us this season but we wish him well on his recall and England's winter tours," Stars coach David Hussey said.
"We're glad Andre was in a position to join us and he'll bring plenty of power and entertainment at the top of the batting order. Andre is a former T20 World Cup winner with the West Indies so he knows what it takes to succeed in major tournaments and I'm confident he'll be a great asset around our group."
Fletcher has played 200 T20 matches worldwide with extensive experience in the Caribbean Premier League, the Bangladesh Premier League, and the Pakistan Super League. He is likely to be available for the Stars for the regular season up until January 26.
"I'm really looking forward to coming over to the Melbourne Stars and being part of what should be an exciting season ahead," Fletcher said. Hopefully, I can bring my brand of batting and recent form to the Stars during the BBL."