The 51-year-old was attacked in Mount Florida, Glasgow, in the early hours of Sunday.
She needed treatment for facial injuries at the city's Victoria Infirmary following the attack.
Police said that around 12.30am the woman was walking outside the football stadium towards Somerville Drive when the man approached her. It is believed he was at a Christmas party at Hampden.
Police have urged anyone with information or who was in the area of the stadium from 12.30am to come forward.
They should call 101, or Crimestoppers on 0800 555111.