Naz Shah, shadow minister for women and equalities, has written to worldwide development secretary Penny Mordaunt and Tory party chairman Brandon Lewis over Mr Johnson's comments.
The former foreign secretary has been criticised for saying Muslim women wearing burkas "look like letter boxes" and comparing them to "bank robbers".
The outrage follows a newspaper article in which Mr Johnson said he did not want the full-face veil and gown donned by some Muslim women to be banned in Britain but the outfit was "ridiculous" and "weird".
Labour's equalities spokeswoman Naz Shah - who in 2016 said comments that resulted in her suspension from the party were anti-Semitic - has called for Theresa May to take action.
Earlier, Foreign Office Minister Alistair Burt said there was a "degree of offence" in Mr Johnson's comments.
Lord Pickles called for Mr Johnson to apologise, but dismissed suggestions that is comments were comparable to Enoch Powell's Rivers of Blood speech.
She added: "Muslim women should not be a useful political battleground for old Etonians".
But the standoff continued even after Theresa May added her voice to calls for him to apologise - although she swerved questions about whether his comments amounted to Islamophobia.
He revealed on Tuesday he had asked Mr Johnson to apologise.
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But the former top diplomat, who has a reputation for causing controversy and quit May's cabinet last month in protest at her Brexit plan, refused to back down.
After a meeting with the Scottish first minister, Nicola Sturgeon, May told reporters: "I am very clear and the government is very clear about our position on the issue of the burka, which is that women should be able to choose how to dress". It is "oppressive... to expect women to cover their faces", he says.
Tory peer Sayeeda Hussain Warsi, a former party chair and diplomat, accused Johnson of adopting the "dog-whistle" tactics of right-wing firebrand Steve Bannon, US President Donald Trump's former top aide.
The fact that Boris Johnson believes comments like these will help him win the Tory leadership tells you everything you need to know about the Islamophobia problem in the Conservative party.
Several European countries, including France, Belgium and Denmark, have banned face-covering veils in public, but none of Britain's main political parties supports such a restriction.
"A single case of abuse is one too many, and since becoming chairman I have taken a zero-tolerance approach", he said.
"The Prime Minister is in denial".
"It's up to a women how they should dress".
Rabbi Laura Janner-Klausner, Senior Rabbi to Reform Judaism said: "Boris Johnson's overall conclusion, that we should not ban religious face coverings, is right".