The England international was arrested during the early hours of this morning following a confrontation outside a club in Yarm, near Middlesbrough.
"Police were called to an incident at a pub on Yarm High Street," confirmed a police spokesman.
"A 27-year-old man has been arrested on suspicion of assault and a 32-year-old woman has also been arrested on suspicion of assault.
"Both are in custody and inquiries are ongoing."
Downing joined the Reds in the summer from Aston Villa.