No pollution was reported, though the platform 17 miles off Galveston sustained significant damage. None of the 16 Russians aboard the freighter was injured.
Crews from two offshore supply vessels were able to put out the flames on the platform, owned by Houston-based EOG Resources Inc., the Coast Guard said.
The ship, the SCM Athina, had superstructure damage and scrapes to its hull.
The platform is a transfer point for various pipelines. By mid-morning, officials said all lines connected to the platform had been secured.
The ship was heading out to sea and carrying containers of general freight. The Coast Guard identified its owner as Sudkap Shipping Co. and the ship is registered to the Caribbean island nation of Antigua and Barbuda.