The turmoil was said to have started after the manager of the Havana Club in St Helier, Jersey, asked the girls to "go away and lose some weight".
Georgina Mason, 23, who was among the group, said that the ban left her feeling "disgusted".
"About five or six or us got there about 11.30pm on Saturday and the bouncers said we were not allowed in because we were too big," the Mirror quoted her as saying.
"I told them not to be ridiculous and asked to speak to the manager. He would not look at me directly but said they'd received too many complaints about fat people. He told me to 'go and lose some weight before you come in - fat people are bad for business'.
"I was disgusted he had the nerve to say this. My friend, who is only a size 14, was not allowed in either," she added.
Helen Warner, who witnessed the storm outside the club, said that she would never set foot in the club again.
"I heard the manager say 'Go away and lose some weight, love'. I can't believe what happened," she said.
As many as 20 women have complained to the police, and set up a Facebook protest page.
Manager Martin Sayers defended his controversial decision.
"We got a lot of people that I'd classify as morbidly obese and we were getting complaints. I am deeply apologetic but business is not good at the minute and I was trying to protect my business," he said.
"If this highlights the problem of obesity, then perhaps some good has come of this. I am overweight myself. I did not do this to hurt anyone," he added.