Henson was arrested by Athens-Clarke County police early Saturday morning for public defecation and public intoxication, while Baldwin, a backup safety, was involved in an altercation outside a downtown Athens bar.
It's the second such offense for both players.
Henson was forced to miss the Sugar Bowl game against Hawaii after being charged with DUI. Baldwin was arrested in January for DUI and was already serving a one-game suspension.
"This is the second incident for both of these young men in the last year," said Richt. "In my judgment their standing with the program is in question and they don't deserve to report with the rest of our team on Sunday."
Baldwin has not been a starter but has played in 20 games during his two-year career while Henson has been Georgia's primary snapper on punts the last two seasons.
For the time being, senior Bo Fowler is expected to replace Henson as the team's long snapper.
According to the Athens Banner-Herald, the Athens Clarke-County police stated that Baldwin and freshman linebacker Marcus Dowtin were hit in the head with bottles following an incident at a downtown bar.
The paper said both players were treated for their injuries at St. Mary's hospital. No arrests were made.
There was no word Saturday night whether Dowtin will be disciplined for his role in the altercation.
Former Bulldog Michael Lemon was also arrested for underage consumption of alcohol. He was dismissed from the team last month for felony aggravated battery.
Lemon was released on a $500 bond while Henson was released on a $750 bond.
Henson's arrest makes eight Bulldog who have been charged in incidents this year.
Others include offensive guard Clint Boling is serving a one-game suspension for reckless driving, while backup fullback Fred Munzenmaier will miss two games for underage consumption of alcohol.