Chika Amadi, a pastor and charity worker and who sits on Harrow council, came under fire after sharing a post from a Christian website.
The 2014 LifeSiteNews.com article showed a picture from a Toronto Pride march with a young girl appearing to cover her eyes as a naked man walked past.
Mrs Amadi tweeted: "Walking about naked in front of children is nothing but paedophelia being labelled liberalism."
I do not talk to expired people. Try me try my God. Walk naked in front of my child, You will know whether you are normal or not. https://t.co/veAmkuIz6A— Chika Amadi (@chikadreams) July 30, 2017
Responding to a user that accused her of "homophobia", she said: "Evil. If you dare walk naked in front of my child God will give you terrible assignment that will put you to perpetual sleep. Be warned."
On her Facebook page last month, Mrs Amadi also posted: "Recently one respectable man in my constituency questioned me on my faith especially on homosexuality (...) I warned him not to try me next time.
"Anyone who wants to bring me down from my political career because of my faith and stand on the word of God will encounter the burning anger of the God that I serve."
In a comment underneath Mrs Amadi's post, a Facebook user wrote "Vultures will eat their flesh", to which she responded saying "Amen. Thank you for standing with me and others in that circumstance".
A Labour spokesperson said: "Chika Amadi has been suspended from the Labour party pending an investigation."
Ian Dylan Thomas and Sarah Kerton, the co-chairs of LGBT Labour, also issued a statement calling her comments "offensive, distasteful and homophobic".
The statement also included: "These comments have no place in modern society and are unacceptable from a Labour party councillor."
They called for Harrow council's Labour group to suspend Mrs Amadi and for her to be reported to the party's standards committee.
Mrs Amadi, who describes herself as a legal adviser, pastor and author, has been a councillor for the Edgware ward since 2014.