The Prime Minister's remark came after several MPs drew upon the memory of Ms Cox when urging him to curb his "violent" and "dangerous" language.
Labour's Paula Sherriff, MP for Dewsbury, criticised Mr Johnson for his repeated use of "Surrender Act" when describing legislation designed to prevent ministers forcing through a no-deal Brexit on October 31.
She warned against using such language and mentioned Ms Cox before highlighting that many MPs are subject to death threats and abuse.
But Mr Johnson labelled her remarks "humbug", which prompted an angry response in the chamber - with shouts of "shame" emerging.
Labour's Tracy Brabin, MP for Batley and Spen, who was elected to the seat after Ms Cox was killed by a man with far-right sympathies during the 2016 EU referendum campaign, also called for the PM to moderate his language.
She said: "As the woman who has taken over a seat left by our dear friend Jo Cox, can I ask him in all honesty as a human being please, please will he going forward moderate his language so that we will all feel secure when we're going about our jobs."
Mr Johnson replied: "Of course there will be an attempt to try to obfuscate the effect of this Act, but it does - the Capitulation Act, or the Surrender Act or whatever you want to call it - it does, I'm sorry, but it greatly enfeebles, it greatly enfeebles this Government's ability to negotiate.
"But what I will say is that the best way to honour the memory of Jo Cox and indeed the best to bring this country together would be, I think, to get Brexit done."
Earlier, Ms Sherriff said the PM had "continually used pejorative language to describe an Act of Parliament passed by this House".
She added: "We should not resort to using offensive, dangerous or inflammatory language for legislation that we do not like and we stand here under the shield of our departed friend with many of us in this place subject to death threats and abuse every single day.
"And let me tell the Prime Minister that they often quote his words Surrender Act, betrayal, traitor, and I for one am sick of it. We must moderate our language and it has to come from the Prime Minister first."
She added: "He should be absolutely ashamed of himself." Her words prompted applause from the opposition benches.
Mr Johnson said: "I have to say Mr Speaker I've never heard such humbug in all my life."
As the PM was heckled, Speaker John Bercow intervened to say: "I appeal to the House as a whole to debate these issues calmly."
Brendan Cox, widower of murdered MP Jo Cox, wrote on Twitter: "Feel a bit sick at Jo's name being used in this way.
"The best way to honour Jo is for all of us (no matter our views) to stand up for what we believe in, passionately and with determination. But never to demonise the other side and always hold onto what we have in common."
Liberal Democrat leader Jo Swinson said in a statement: "To suggest the best way to honour Jo Cox, an MP who was murdered for what she believed in, was to pass his Brexit deal was sickening.
"The office of Prime Minister is one that should seek to lift our debate and show the best of our Parliament. Boris Johnson demeaned that office with his words today, and he should apologise immediately for them."