The news was first reported by television station WOIO in Cleveland.
Manziel was cited at 8:28 a.m. in North Olmsted, Ohio. He has an arraignment on Jan. 21, but he can pay $125 online to waive the charges.
North Olmsted is close to Cleveland Airport but also close to Berea, where the Browns' facility is located.
Manziel was in the NFL concussion protocol at the time he was cited. He was placed in it on Dec. 30.
On Sunday, he failed to report in the morning to the team facility for a required assessment. Reports said he was in Las Vegas on Saturday and Sunday.