Daniel Kawczynski, MP for Shrewsbury and Atcham, said he had written to chairman of the party's 1922 Committee Graham Brady, asking for him to look into the matter.
It was revealed last week that Mr Banks, who co-founded the pro-Brexit campaign group Leave.EU, had his application for Conservative Party membership rejected.
Theresa May was reported as saying that Mr Banks's membership had been rejected because he had previously campaigned against the Conservative Party.
The insurance tycoon had previously been one of Ukip's biggest financial backers.
But this week he urged all 90,000 members of Leave.EU to join the party so they could vote in the party's next leadership election.
However, Mr Kawczynski said the Conservative Party had a long tradition of accepting people how had previously been members of other parties, and could not understand why Mr Banks had been singled out.
"The Conservative Party is not an exclusive club," he said.
"People should be allowed to join as long as they have not broken the law or done anything that could bring the party into disrepute.
"I have asked the chairman of the 1922 Committee, who is effectively our shop steward, to ask if he will formally investigate whether the Conservative Party has broken any of its own internal rules.
"Theresa May has said it is because he has campaigned against the Conservative Party in the past.
"But we have allowed former Labour and Lib Dem and Ukip councillors and MPs to defect and join our party, so what is the difference? There's a big inconsistency here."
Mr Banks told the Westmonster website, which he founded, that he was joining the Tories because he believed a leadership battle was coming soon.
“We believe that the battle for Brexit is now within the Conservative party,” he said.
His business partner and Leave.EU co-founder Andy Wigmore also had his application rejected. Mr Wigmore said he wanted to join the Conservatives “to ensure that if there is a leadership contest then I can influence the type of leader the country and the Tory party need”.
He added: “We need a Brexit leader, one who believes in Brexit and will deliver what 17.4 million people voted for.”
Pro-EU Tory MP Anna Soubry claimed the party was being 'infiltrated' by Brexit campaigners.
But Jacob Rees-Mogg, a prominent eurosceptic who once stood to become MP for The Wrekin, pointed out that before joining the Conservatives Miss Soubry had been a member of the Social Democratic Party.