The member for Fylde in Lancashire disputes the allegations reported by The Times but the party said he had agreed to have the whip withdrawn, meaning that he will now sit in the Commons as an independent.
Mr Menzies became the eighth Tory MP to be suspended over various allegations including of sexual misconduct.
He denies any wrongdoing.
Defence Secretary Grant Shapps denied that suspect behaviour was rampant in his party's ranks after 14 years of Conservative rule.
He told LBC: "There are people I'm afraid in every walk of life who either won't do the right thing or sometimes are troubled individually, perhaps with mental health and other things which leads them to do things which they shouldn't have done. Those eight aren't all sitting in Parliament."
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