Lafayette County Sheriff's Department records show Speaks was arrested just after midnight and released at about 7 a.m., according to The Associated Press.
"Breeland's poor choice does not meet the expectations of our program, and there will be consequences," Ole Miss coach Hugh Freeze said in a statement obtained by ESPN. "He and I have spoken, and he is very disappointed in himself and will accept whatever punishment that is handed down.
"We are very thankful he is safe and that this was not a life-altering decision. In these situations, we hope our young men learn from their mistakes and do not let the mistake define them."
Speaks played in all 13 games last year -- starting two -- and finished with 32 tackles, 5.5 tackles for loss and one sack. The redshirt sophomore was among those expected to compete for a starting job and fill the void left by star defensive tackle Robert Nkemdiche.
The Associated Press contributed to this report.