According to the U.S. Coast Guard, the report came in just before 11pm Friday.
The M/V Ashton T, a 94-foot offshore supply vessel, ran aground on the Galveston North jetty.
The Ashton T was carrying about 1,650 gallons of diesel fuel when it ran aground, officials said.
Authorities said one crewmember suffered minor injuries and was transported to an area hospital. There was no damage to the Ashton T's fuel tanks and there have been no reports of pollution.
USCG Cmdr. James Robertson with Marine Safety Unit Texas City announced in a release Saturday that there were no major injuries and an effort to remove the vessel is underway.
"We are working in concert with the vessel owners, T and T Marine, to safely and quickly remove the vessel with no impact to the environment," Robertson said.
The cause of the grounding is under investigation.