The arrests happened at the Union Springs Country Club Tuesday night.
The ABC board says agents obtained a search warrant after a months-long investigation into the games. When agents arrived at the club, they found a game already in progress.
Agents also recovered containers of moonshine whiskey and privately manufactured wine.
Six of the men arrested face simple gambling charges, and a seventh faces charges of promoting gambling.
Those arrested include: Randall Hall, Darron Web, Joe Stuart, Henry Capps, Charlie Pinson, William Chancellor and Jimmy Duncan. Duncan was the individual charged with gambling promotion.
Each of the suspects was arrested, transported to the Bullock County Jail.
The case is ongoing, said the ABC Board in a statement. Prosecution will be handled through the Bullock County District Attorney's office.