Sandwell councillor Steven Frear wrote the post alongside a link to the BBC story on the death of the former Prime Minister.
Within minutes of his post there was a flurry of angry responses to what the Bristnall ward councillor had written. He later issued an apology on the site.
Even after the post was removed, debate raged on his Facebook page, with some suggesting the councillor should stand down after his comments.
Wendy Ainge wrote: "That's not nice, the woman is a mother and a grandmother", while Heather Wagstaff added: "That's a vile thing to say about a woman that is still a human being wouldn't expect anything less from a labour candidate."
Nise Mc Goldby-Timmis responded: "Harsh Steven!!" and a Donna Ronankeating Wimbush said: "have to agree, a bit harsh."
Councillor Frear of Hill Top Road, Oldbury initially posted on his open page: "It's a song Wendy" in response to the angry comments, but later deleted it completely.
He then apologised for his Facebook comments on his page and wrote on the site: "Sorry for post earlier, it was insensitive, out of order and wrong. I express my condolences to her family."
Council leader Darren Cooper said: "Feelings are running high and I do think Councillor Frear's comments were insensitive and wrong. I was pleased to see that he swiftly took it down and apologised."
The storm refused to abate after the apology. A Tracy Barnes wrote: "It is a total disgrace..as someone who has lost her mother I thought it was disgusting."
Gary Pollard told Councillor Frear on the site: "You should stand down from your role after such a comment." Whereas others backed Councillor Frear's post a Dave Waldron wrote: "O grow up! I bet you were jumping for joy when they got old Osama and Saddam! What he said shows why this country is great, FREE SPEECH!"
A Peter Blackcountry Rowley said: "No need to apologise" and a Tina McLeod said: "She stood for personal freedom so she would object to people feeling they couldn't openly express their opinions."
Councillor Frear who was first elected in May 2006 and chairs Sandwell Council's planning committee, as well as sitting on the Oldbury scrutiny panel and joint consultative panel was unavailable for comment.