Manziel was involved in an incident with former girlfriend Colleen Crowley on Jan. 30 in Dallas. She said the 2012 Heisman Trophy winner forced her into his car and hit her repeatedly, resulting in a ruptured eardrum.
The charge could carry up to one year in jail and a $4,000 fine.
"The investigation of the domestic violence assault involving Jonathan Manziel, which occurred on January 30, 2016, has been completed," the Dallas police department said in a statement released Thursday. "Today, a Class A misdemeanor Assault/Domestic Violence case has been referred to the Dallas County District Attorney's office for presentation to the grand jury. The Dallas Police Department will not release any details of the investigation while it is pending grand jury presentation."
In an interview with TMZ, Manziel denied hitting Crowley. But the Browns apparently are ready to release Manziel next month.
"His future on our team will be addressed here pretty soon," Browns coach Hue Jackson said at the NFL Combine on Wednesday. "But let me say this: I think it's really important that obviously there were some people involved in the situation that happened and I feel very bad about those things as they do happen.
"But I want to make sure we all understand that that behavior will not be tolerated as we move forward, and that's all I want to say about it. Our organization is going to take a stand, and we're going to move on from those kind of situations as we move forward."
Maj. Midge Boyle, a Dallas police spokeswoman, said investigators reviewed medical records and video surveillance from that night.
Crowley said in an affidavit that she tried to escape but couldn't and the two struggled inside the vehicle on their way back to her Fort Worth apartment.