The 26-year-old model is said to have been involved in a scuffle with another woman at the Panacea nightclub in Alderley Edge, Cheshire in January.
"She was on a night out with a couple of friends and ended up having an argument with another girl who had sneaked into the VIP area and became a nuisance," a friend of Clancy's told The Sun.
"All she did was tweak the girl's hair, which sparked the complaint to security. The police showed up and sorted it all out but Abbey felt she had been targeted because she is well known.
"There have been problems since, which Abbey has been trying to ignore."
A spokesman for Cheshire Police confirmed the report, saying: "A 26-year-old woman from Macclesfield was given an adult caution."
Clancy recently revealed that her daughter's first birthday made her emotional.
The Britain's Next Top Model star welcomed her first child with footballer Peter Crouch last year.