The body of Janice Farman, 47, who is originally thought to be from Clydebank, West Dunbartonshire, was found at a property in Albion on the island at 1am on July 7.
Police said the 18-year-old man from Quatre Bornes was arrested on Thursday.
It follows an appearance by two 25-year-old men in court on Tuesday charged with her murder.
A spokesman for the Mauritius Police Force said the investigation was “progressing” and the third suspect Anish Sonnea, 18, was arrested on Thursday.
He said: “He appeared in court this morning and has been remanded until July 21.
“The two other suspects have been remanded until July 18. The investigation is progressing.”
Ms Farman was working as managing director for data capture firm PECS Data Services in Mauritius before she was murdered.