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.
"Things are improving in the north of La Reunion island but ... not on high points in the west," prefect Patrice Latron said, pointing to heavy rainfall.
The prefecture had 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.
The prefecture said the worst of the storm had passed and a storm alert had been downgraded from the highest level - purple - to red.
This meant rescue workers could 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.
Top winds had dropped to 130km/h, Meteo France said, but higher gusts were possible on the southwest of the island, with heavy rains seen as a bigger risk.
In nearby Mauritius, authorities reopened the airport after the threat from the storm eased.
