Prefect Michel Lalande followed other territories in the region in declaring the medium-level alert for the island, an overseas department of France that is east of Madagascar and has a population of about 800,000.
The prefecture said in a statement that the tsunami could hit the island's shores between 7:00 pm and 8:00 pm local time (1500 and 1600 GMT). It said local authorities and emergency services were on alert and that swimming would be banned.
It urged local residents to use "the greatest caution."
"A tsunami is not a show, get to an elevated position, far from theshoreline," it said.
Réunion suffered some damage during the 2004 tsunami in the Indian Ocean, with the loss of several fishing and pleasure boats.