The ASA said they were likely to cause offence and “portrayed all beggars as disingenuous”.
The council said it might appeal against the decision.
More than 2,000 people signed a petition criticising the council for “vilifying” the homeless with the messages “begging: watch your money go to a fraud” and “watch your money go up in smoke”.
The council reworded the posters for a second phase of the campaign, but one of these was banned.
The ASA investigated after seven people complained the posters portrayed homeless people in a derogatory manner and implied that all homeless people were engaged in criminal and anti-social behaviour.
The authority said the language used in the adverts “portrayed all beggars as disingenuous and undeserving individuals that would use direct donations for irresponsible means”.
It added: “We further considered the ads reinforced negative stereotypes of a group of individuals, most of whom were likely to be considered as vulnerable, who faced a multitude of issues and required specialist support.”
The council said the posters were not about homeless people and claimed most people who beg do not sleep on the streets.
Councillor Jon Collins, leader of the Labour run authority, said he was considering calling for a review of the decision.
He said: “The posters needed to be hard-hitting to get such a serious message across effectively. There’s no point in running a campaign that no-one is going to take notice of.”