West Midlands Labour said it was “extremely concerned” about the incident and suspended both councillors from the party “immediately”.
The party said it would not be commenting further because of the ongoing police investigation.
A spokesperson for West Midlands Police said it was called after a report of an assault in the early hours of Sunday morning on Surfeit Hill Road.
A West Midlands Ambulance Service spokesperson said it was called to the street at about 02:50 BST.
They added: “On arrival crews found two men who they treated for injuries not believed to be serious before conveying them to hospital.”
A spokesperson for West Midlands Labour said: “Both councillor Millard and councillor Mayo were administratively suspended by the Labour Party immediately upon receipt of these allegations.
“Given this is subject to a police investigation we are not able to comment further at this time.”