Hugh Vaughan and his wife Liz lived in Prees Heath, near Whitchurch and had been on holiday on the island.
Mr Vaughan was the UK director of Landia UK – which supplies machinery to farmers across the UK from its base in Whitchurch.
A statement on Landia’s website says: “It is with deep sadness and shock that we have to report the untimely death of Hugh Vaughan, director of Landia UK, who together with his wife Liz passed away after a road accident whilst travelling in a taxi during their holiday in Mauritius.
“As the head of Landia UK since it was established in 1994, Hugh has guided the company to its position now as a highly reputable and continually growing manufacturer of top quality pumps and mixers.
“Hugh will be sorely missed. We send our heartfelt sympathies to Hugh and Liz’s families.”
The Foreign Office said it is supporting their family and remains in contact with the Mauritian police.
A Foreign Office spokesman said: “We are supporting the family of two British people who have died in Mauritius.
“We remain in contact with the Mauritian police.”