Snelling is expected to rejoin the Falcons on Monday.
"We are disappointed in what has transpired over the last 48 hours concerning Jason Snelling," Smith said Saturday in a statement. "Any time one of our players is involved in an off the field incident we take it very seriously. Jason missed practice on Friday.
"After speaking with him yesterday, Jason has decided to take some personal time to deal with his situation and will miss tomorrow's game. We anticipate him rejoining our team Monday morning."
Snelling has played in eight games for the Falcons this season and has 36 rushes for 132 yards with three total touchdowns.