The complaint claims the comments breach a clause that forbids members of parliament from actions which “cause significant damage to the reputation and integrity of the House of Commons”.
Helen Grant, the Tory vice chairwoman for communities, said the comments had been branded “xenophobic and anti-Semitic”.
Mr Corbyn made the comments at a conference in 2013, and a video of the event was found and published by MailOnline.
He discussed a speech by the then Palestinian ambassador, Manuel Hassassian, which he says was recorded by “thankfully silent Zionists” who then approached the speaker and “berated” him.
Referring to the “Zionists” he says: “There are two problems, one is they don’t want to study history, and the second is, having lived in this country for a very long time, probably all their lives, they don’t understand English irony either.”
Zionism is the support for the creation of a Jewish homeland in the state of Israel. Many who use the term stress that the word does not refer to all Jewish people, but critics say it can function as a coded reference to Jews.
Critics of Mr Corbyn said his comments were racist and appeared to undermine Jewish people’s place in the UK.
Labour MP Luciana Berger said the “inexcusable comments… makes me as a proud British Jew feel unwelcome in my own party”.
She added: “I’ve lived in Britain all my life and I don’t need any lessons in history/irony.”
Following outcry over the incident, Mr Corbyn has defended the words, saying: “I described those pro-Israel activists as Zionists, in the accurate political sense and not as a euphemism for Jewish people – and that is made clear in the rest of my speech that day.
“I am now more careful with how I might use the term ‘Zionist’ because a one self-identifying political term has been increasingly hijacked by antisemites as a code for Jews.”
He said he was attempting to “defend the Palestinian ambassador in the face of what I thought were deliberate misrepresentations” from people “for whom English was a first language, when it isn’t for the ambassador”.