British Airways has held the stake since 1973.
"We invested in the airline when it was a startup airline. It is now a successful carrier, operating to the highest standards and no longer requires our involvement and support," said Robbie Baird, British Airways' area general manager for Asia Pacific.
"I'm pleased to say that this sale has been done with the full cooperation of Air Mauritius and the Mauritian government," Baird said.
BA is selling its 3.84 per cent share in Air Mauritius Ltd to the Mauritian government and its 13.24 per cent share in Air Mauritius Holding Co. Ltd. To existing shareholders.
The sale should be completed in July, the airline said.