"The man refused to be arrested and fired a rifle at police," a local government official on the island said.
The official said that the suspect -- a man in his twenties who is believed to be a recent convert to Islam -- was now in custody.
The lives of the two officers are not in danger.
The anti-terrorist department of the Paris prosecutor's office is investigating the attack, which occurred in the Saint-Benoit arrondissement to the north east.
The attack on Reunion comes a week after a French policeman was shot and killed and two others wounded on Paris' Champs Elysses avenue. That attack was claimed by the Islamic State group.
More than 230 people have been killed in a string of jihadist attacks on the French mainland since January 2015.
A jihadist network, the first in a French overseas territory, was smashed in Reunion in June 2015. Its leader, a 21-year-old known as "The Egyptian", was arrested and transferred to Paris.
Authorities in Reunion estimate there are around 100 radicalised Islamists on the island.
The local government official said Thursday's assailant was also "suspected of being radicalised".
France's police union Unite SGP POLICE-FO said it was "deeply shocked and angry after this new attack."
It "shows that policemen are in danger throughout the national territory and not only in certain areas as judges would have us believe," it added.