Stiehl identified the 47-foot tug boat as the Shanon E. Settoon. Settoon Towing of Pierre Part, La., lists the tug boat among its vessels on its website.
The Coast Guard said ES&H has been hired to handle the oil spill response.
It was not immediately known who owns the 154-foot oil barge.
The area is thinly populated and no evacuations have been ordered.
"We are aggressively responding with our state and local partners to mitigate the fire and prevent any potential impacts from oil that entered the water," Coast Guard Cmdr. Russ Bowen said in a news release.
The area is along the northern reaches of Barataria Bay, which was heavily affected by oil from the BP spill in 2010. It is mostly small communities where people often make their living from the sea, either working in the oil and gas industry or as fishermen.
The 92,000 gallons the Coast Guard says was being carried by the barge is a fraction of the millions of gallons that spewed into the Gulf of Mexico during the 2010 spill.
The region where the fire was burning is criss-crossed by pipelines and wellheads are a common sight in the shallow waters of the bayou and bay shoreline.
Bayou Perot was the scene of an explosion and fire on a specialized oil rig in December 2010 in which three men were injured. The explosion happened while the men were welding and there was no pollution, the Coast Guard reported.