Kelley, 20, played in Arkansas' 33-10 loss at LSU on Saturday, completing 3 of 10 passes for 33 yards with an interception. According to online court records, he was booked at 8:47 a.m. CT at the Washington County jail and has a hearing scheduled for Monday.
Kelley was released on bond Sunday.
"I was informed early this morning of an incident involving Cole Kelley," Razorbacks coach Bret Bielema said in a prepared statement. "We are gathering all information from the proper authorities and will make a determination upon review of that information."
Kelley, ranked by ESPN as the nation's No. 16 quarterback in the 2016 recruiting class, sat out last season but has appeared in nine games this season, completing 87 of 151 passes for 1,038 yards with eight touchdowns and four interceptions.