The 'Mac' drawing, featuring caricatured men with exaggerated noses and veiled women crossing the border into Europe, accompanied by rats scurrying across the floor, inflamed tempers.
"To me, and to many of my constituents, Muslims and non-Muslims alike, this cartoon appears to be Islamophobic," he wrote to tabloid boss Paul Dacre.
"And, what is more, comes at a time when our country's Muslim community - which was as shocked and saddened as we all were at the unforgivable atrocities in Pairs - feels under threat of demonisation."
It was published on Thursday by an unofficial group campaigning for Jeremy Corbyn to become UK Prime Minister.
Press standards regulator 'Ipso' confirmed it had received 200 complaints regarding the drawing, prompting speculation by some on social media that Mail editors may face an investigation into its publication.
But the Mail's managing editor's office said in a statement that they would refuse to deny "absurd" allegations with a reply.
"We are not going to dignify these absurd comments, which willfully misrepresent this cartoon, with a response," they commented.
"As should be blindingly obvious, Mac’s cartoon is a comment on the terrorist atrocities in Paris. The rats were intended to depict terrorists smuggling themselves into Europe amongst innocent refugees."