It was the second time Henson was arrested and suspended for alcohol-related incidents. He also missed last season's Sugar Bowl after a DUI arrest.
The future of defensive back Donavon Baldwin, who was suspended after an unrelated altercation the same night as Henson's arrest, remains in limbo.
"Jeffrey will not be returning," Richt said. "I'm still working on Donavon. I'm getting really close."
Baldwin was injured in a fight at a downtown Athens bar the weekend before fall camp opened. He was treated, along with teammate Marcus Dowtin, for injuries after he was hit with a bottle, and Bulldogs linebacker Darius Dewberry was also suspended for damaging property at St. Mary's Hospital after the incident.
Dewberry returned to action last week against South Carolina. Senior Bo Fowler has taken over as the starting snapper in Henson's absence.