Health Secretary Jeremy Hunt said the Cabinet Office would be carrying out an investigation into whether the Ministerial Code of Conduct had been breached.
“These stories, if they are true, are obviously totally unacceptable,” Mr Hunt told BBC1’s The Andrew Marr Show.
Mr Hunt said Theresa May would also be writing to Commons Speaker John Bercow to ask for his advice on how the culture at Westminster could be changed.
“There are mums and dads who have daughters who are politics students hoping to get a job in Westminster and they must be able to be confident that if they get that job, their daughter will not be subject to some of these behaviours that we have been seeing,” he said.
Mr Garnier’s former secretary Caroline Edmondson told The Mail on Sunday that the married MP had given her the money to buy two vibrators at a Soho sex shop - one for his wife and one for a woman in his constituency office.
Ms Edmondson, who has since left to work for another MP, said that on another occasion, in front of witnesses, he called her “sugar tits”.
The Mail said Mr Garnier had admitted the claims, saying: “I’m not going to deny it, because I’m not going to be dishonest. I’m going to have to take it on the chin.”
According to the paper, he said the “sugar tits” comment was part of an “amusing conversation” about the TV comedy Gavin And Stacey, while the sex toys were bought after a Christmas lunch.
“The vibrator shop was high jinks. I hung around outside and she went into this shop. That was it,” he is quoted as saying.
The Mail said Mr Garnier had conceded that, in the current climate, his actions could look like “dinosaur behaviour”, but insisted: “It absolutely does not constitute harassment.”
In a separate case the Mail said former cabinet minister Stephen Crabb had admitted sending “explicit” messages to a 19-year-old woman he interviewed for a job in 2013, when he was a Welsh minister.
The married MP was quoted by the paper as saying he had been “foolish” but that there had been no sexual contact.
“We exchanged messages which talked about sex but none of it was meant seriously,” he was quoted as saying.
“We met for coffee a few times and had a glass of wine once at the Commons, but nothing more.
“I accept any kind of sexual chatter like this is totally wrong and I am sorry for my actions.”
Mr Crabb resigned last year as Work and Pensions Secretary following reports of a similar incident.
Former Tory opposition whip Owen Paterson said if there was an allegation of a legal offence the Whips’ Office should take it further.
He told Sunday with Paterson on Sky News: “I think it depends on the severity of the offence or the activity - in some cases, some of these recently reported activities, obviously totally inappropriate but the individuals concerned have apologised.
“But there might be, for all I know, offences which are more serious in which case perhaps the Whips’ Office should take it further.”
The former cabinet minister added: “It is obviously incumbent on Members of Parliament to behave properly but, as I said, there are certain areas where I think an admission of guilt and a full public apology is right, but if the whips are privy to much more serious allegations where an actual legal offence might have been called, perhaps they then have to take it further.”