The cyclone made landfall in the north of the Indian Ocean island, which lies off Madagascar, blowing away roofs and cutting power and access to drinking water for many residents. It exited the southwest of the island several hours later, Meteo France weather agency said.
Meteo France said the worst of the storm had passed on Friday.
The storm alert was downgraded from the highest level, purple, to red, earlier in the day, which allowed rescue workers to leave their shelters and start to assess damage and help those affected.
A mandatory order for residents to stay indoors remained in place and authorities expected rough weather conditions until at least the end of the day.
"The cyclone is still a threat for the island, I call on all to follow local authorities' instructions," Bayrou said on X.
The prefecture said earlier that 180,000 households - about 42 per cent of the electricity utility's customers - had lost power, and nearly 10 per cent had no access to drinking water.
Wind speeds had dropped, Meteo France said, but 80-100 km/h gusts were possible overnight, with heavy rains now seen as a bigger risk. Weather conditions should improve on Saturday.
In nearby Mauritius, authorities reopened the airport after the threat from the storm eased.
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