Cllr Shirley Brown made the comments last February
A Bristol councillor who insulted her rival with the racial slur "coconut" has been suspended for a month.
Black Liberal Democrat Shirley Brown called colleague Jay Jethwa, who is Asian, a coconut during budget debate in February.
The term suggests someone from an ethnic minority has "sold out" their culture, implying they are "brown on the outside, white on the inside".
Cllr Brown, who has apologised for the remark, was suspended on Tuesday.
She used the term during a heated debate over a Tory attempt to cut funding to the Legacy Commission, an organisation set up to support Bristol's ethnic minorities.
She told Mrs Jethwa at the meeting: "In our culture we have a word for you, a word which many in the city would understand, and that's coconut.
"At the end of the day I look at you as that."
The council investigation was launched after complaints from Conservatives and members of the public.
Councillor Jethwa told the committee: "It is extremely insulting for councillor Brown to suggest I am not aware of my culture.
"I urge the strongest sanction possible is taken to send the message that racism from any quarter will not be tolerated in this city."
In her summary, committee chair Anne Foot said: "This committee condemns without reservation the deeply offensive language.
"Whilst there could have been far worse examples of abusive language these particular words were aimed to cause offence and in fact caused offence.
"The undoubted fact is that this behaviour has resulted in damage to the council's reputation and the reputation of the role of councillor.
"We would hope that councillor Brown has learnt a very painful lesson and would not use offensive language again."
Cllr Brown has since apologised for using the term, and repeated her apology to the committee.
She said: "I am sincerely sorry. It was never my intention to hurt, harm or bring any disrepute to the council. We all use different terminology in our culture, unfortunately I used the wrong terminology. It was never my intention to offend. I should not have said it."
She now has 21 days to appeal against the decision to the Standards for England, the government's local authority ethics watchdog.