East Riding councillor Dominic Peacock made an offensive remark donating to the appeal.
He was responding to a news story about the appeal following Mrs Cox’s death reaching £1 million when he posted on Facebook: “I’ve just donated the steam off my p***.”
In a follow-up post, responding to critics, Coun Peacock wrote: “I am sick and tired of this woman’s death being used against the Brexit cause.”
Soon after, he posted on a local Vote Leave supporting page: “I’ve deleted my offensive comment I shouldn’t have put it on in the first place - I won’t make excuses.”
Coun Peacock is one of three Tories who represent the Minster and Woodmancy ward, which covers the countryside just north of Hull, on the Conservative-run council.
Stephen Parnaby, East Riding Council and Conservative group leader, said the councillor had been suspended from the group with immediate effect for “inappropriate and offensive remarks.”
He said he would recommend that Coun Peacock be expelled.
Coun Parnaby said: “Following inappropriate and offensive comments made on social media relating to the sad and tragic death of Jo Cox MP, I have suspended Coun Dominic Peacock from the East Riding of Yorkshire Council Conservative Group with immediate effect. I shall be reporting this to a meeting of the full Group and my recommendation will be that he be expelled.
“All people in public life, irrespective of politics should be united in condemning the fatal and dreadful attack on Jo Cox. This is not the time for inappropriate remarks, however intended, and I will not tolerate them in my Group, and residents should expect their elected representatives to act in an appropriate and compassionate way.
“I will also be asking the Group to make a contribution to the Memorial Fund set up in the name of Jo Cox.”
Coun Keith Moore, deputy leader of the council’s Labour group, told The Yorkshire Post: “I believe he should be expelled from the Conservative party for such insensitive comments and vile language.”
Coun Moore said a meeting of the East Riding Council was scheduled for tomorrow, with a minute’s silence for Mrs Cox part of the agenda.
Beverley and Holderness Conservative MP Graham Stuart said: “I was appalled by Councillor Peacock’s grossly offensive and insensitive post and it is right that he has now apologised unreservedly and removed the post.
“Jo Cox is a huge loss to British politics, was a warm and caring person and leaves behind a devastated family. Councillor Peacock should be utterly ashamed.
“I fully support his suspension from the East Riding of Yorkshire Council Conservative Group.”
East Riding independent councillor Andy Strangeway called for Coun Peacock’s “immediate resignation”.
Coun Peacock has been an East Riding Councillor since 2011 and was re-elected last year. He also sits on Beverley Town Council’s Policy and Grants Committees.
On his council register of interests, he describes himself as a residential landlord, and lists 11 Beverley properties in which he has a “beneficial interest”.