The pair were targeted inside the fast food restaurant on Union Street in Aberdeen at around 3am on Saturday.
The assault continued on the street outside near Greggs at 227 Union Street, just past the junction with Dee Street.
One of the victims, aged 20, suffered a serious facial injury while the other, aged 33, was also injured.
Both were taken to Aberdeen Royal Infirmary.
Police Scotland are keen to trace a man who is described as being white, in his 20s of stocky build, with dark brown hair, cut short on top, shaved at the sides and at the back meeting at a point in the middle in a V shape.
He was wearing a dark coloured jacket, black t-shirt with a white round logo on front and dark jeans with black trainers. He has a distinctive limp.
Police Constable Andrew Watt, of the Alcohol & Violence Reduction Unit said: "At this time, we are piecing together what happened and looking through CCTV.
"We are following a positive line of enquiry, however, Union Street at Dee Street is a busy area, particularly during the early hours of a Saturday morning and I am convinced that someone walking past would have seen the incident.
"I urge anyone who saw an altercation involving this man, or believe they recognise the description provided to contact us immediately."