The Starkville Daily News reported that the 21-year-old Cox was arrested at the scene after Oktibbeha County Sheriff's deputies responded to a burglary call at an apartment complex at 3 a.m. and found a woman with a head injury.
Cox posted a $20,000 bail later Friday.
Bulldogs coach Dan Mullen announced the suspension Friday morning.
Cox, a former junior college transfer, has started eight games this season for the No. 4 Bulldogs and has 21 tackles and an interception.
No. 4 Mississippi State (9-1, 5-1 SEC) hosts Vanderbilt (3-7, 0-6) on Saturday.
The Associated Press contributed to this report.