Coun. Rosemary Carroll, who was the borough's Mayor until last month, shared the racist and derogatory joke on her Facebook page, prompting angry complaints from members of the public and fellow councillors.
The leader of Pendle Borough Council, Coun. Mohammed Iqbal, has made an official complaint and called for the Earby councillor to be expelled.
Coun. Iqbal said: "I have been approached by members of the public regarding the highly offensive posting by Coun. Carroll, and have asked for an urgent investigation as she has broken the code of conduct for elected members.
"It is disappointing to see such a senior councillor agree with such a vile post. I have also written to the Prime Minister and leader of the Conservative group on Pendle Council, Coun. Joe Cooney, asking that she be expelled from the Conservative Party immediately, unless they support and agree with such comments.
"This is not the first instance of Pendle Conservative councillors reported for racist comments, and it appears they have issues with sections of our community."
Pendle Tory leader Coun. Cooney confirmed that Coun. Carroll has been suspended pending an investigation.
He said: "This morning we were made aware of a racist post which had been shared on Facebook by one of our councillors, Rosemary Carroll.
"We will not tolerate racism of any form. Rosemary Carroll has been suspended from the Conservative Group on Pendle Borough Council and the Conservative Party with immediate effect, pending a full investigation in due course."
Philip Mousdale, Pendle Council’s Corporate Director, confirmed he is investigating the complaints.
He said: “I’ve received two formal complaints under the Councillor Code of Conduct relating to a Facebook post shared by Coun. Rosemary Carroll.
“As monitoring officer for the council I am looking into the complaints."