The allegations were submitted to the Equalities and Human Rights Commission (EHRC) by the Muslim Council of Britain, which called for it to investigate.
The prime minister said: “I can reassure there is absolutely no room for hatred or racism in this party, in our Conservative – and I wish I could say the same of her own party.”
Ms Shah, whose remarks were greeted with cries of “shame” from the Conservative benches, later tweeted: "I won’t be shouted down just because the Conservative party doesn’t want to deal with the rot of Islamophobia that has settled inside their party.”
Jeremy Corbyn had appointed Ms Shah to his shadow cabinet in 2018 as shadow minister for women and equalities.
She was readmitted to the party in July 2016, after she was suspended for comments she made before her election in which she suggested spending “transportation costs” to move Israelis out of the Middle East. In another post that year she appeared to liken Israel’s policies to those of Hitler.
She she made a full apology and vowed to win back the Jewish community's trust.
In another fiery exchange on Wednesday, the prime minister raised antismetism after Mr Corbyn accused him of making sexist remarks in the past.
Mr Johnson said: “I will have no lessons in sexism from a party where good female MPs are bullied out of it just because they have had the guts to stand up against antisemitism.”
