The 19-year-old was pushed to the ground and punched in the face in Glasgow city centre.
She was walking with a 16-year-old when the pair were targeted in St Enoch Square at 1am on Saturday.
Police said they were approached and verbally abused by the man, who punched the victim to the ground.
The suspect ran off after the attack, but police said his clothes and bag may have been torn in the struggle.
The victim was taken to the city's Royal Infirmary where she was treated for her injuries, but later released.
Officers said it had been a "nasty" and unprovoked attack. The male attacker, who has a full-sleeve tattoo, is described as being in his mid to late-20s, 6ft, with ginger hair. He was wearing a white T-shirt and blue jeans and was carrying a black ruscksack.
Superintendent Alan Porte, who is leading the inquiry, said: "This was a nasty attack on two young women. Police Scotland has a zero-tolerance approach to tackling crime based on prejudice and I want to make clear it will not be tolerated.
"In relation to this serious assault, officers have been carrying out inquiries in the local area and studying CCTV in an effort to gather information on the man responsible.
"St Enoch Square may have been busy with people on nights out and I believe passing motorists or pedestrians may have seen something which could help us."
Anyone with information is urged to call Police Scotland on 101. All calls will be treated in confidence.
Last month it emerged the number of reports of hate crimes against members of the lesbian, gay, bisexual and transgender community has risen by 22 per cent in a year., with 890 crimes last year.