It happened around 10 a.m. Thursday.
The Galveston County Sheriff said the man was swimming in the water along Stingaree Drive when he felt a tug. He was bitten above the knee on his right leg.
The victim is at UTMB hospital. We're told he was up and talking. He's expected to be okay.
Authorities shared a photo with ABC13 of what appears to be bite marks.
According to the Florida Museum of Natural History, which is affiliated with the University of Florida, there have been 18 confirmed shark attacks in Galveston County since 1911.
At this time, the sheriff's office does not plan to close the beach.
Warning: The photo below is graphic.