The 31-year-old changed his plea when he appeared at Stained Magistrates' Court on Monday, when his trial was due to start.
The winger admitted to a section 4 public order offence of "using threatening, abusive or insulting words or behaviour with intent to cause fear or provoke unlawful violence."
However, a further charge of beating was dropped after the prosecution offered no evidence to support it.
CCTV footage showed Puncheon lashing out at a doorman with his belt, which had previously been confiscated.
According to Puncheon's lawyer, he had been acting in self-defence after someone had attempted to strike his wife and after his friend had been punched.
The incident ocurred on December 17, neaat the Mishiko bar in Reigate.