Police said they were concerned about Alishba Khan, who was last seen in the Quays area of Gloucester at about 19:30 GMT.
Alishba is considered "vulnerable" due to her age and other factors.
She is not thought to have been abducted, but the motives of the man she left with were "unclear", police said.
Gloucestershire Police said Alishba met the man after asking a number of people in the area for cigarettes.
He gave her a cigarette, and the pair left together, police said.
Alishba, who has only been in Gloucester for a week, is 5ft 6ins (1.68m) tall, of stocky build, with long black hair in a ponytail.
She was wearing a green parka jacket with fur in the hood, blue jeans, black ankle boots and was carrying a black handbag when she went missing, police said.
The man was about 5ft 8in (1.73m) tall and of slim build. He was on a white mountain bike with Concept written on the frame.
He was wearing Adidas black tracksuit bottoms, a black jacket, a black baseball cap and was carrying a Nike rucksack.
The force says anyone who sees Alishba should dial 999 immediately.
A 12-year-old girl seen leaving a shopping centre with a stranger has been reported missing.