The Cabinet Office -- responsible for ensuring effective government -- will investigate if Mark Garnier's behaviour violated ministerial codes of conduct, Health Secretary Jeremy Hunt said on Sunday.
"These stories, if they are true, are obviously totally unacceptable," Hunt told a BBC political programme.
A Cabinet Office spokeswoman confirmed the investigation into Garnier -- a married father of three -- but declined to comment further.
Garnier's former secretary Caroline Edmondson told The Mail on Sunday newspaper that the Conservative party lawmaker gave her money to buy two vibrators from a London sex store in 2010.
The paper also reported that Edmondson, who now works for another lawmaker, said Garnier also described her in lewd terms on one occasion, in front of witnesses.
Garnier, who could not be reached by AFP for comment on Sunday, admitted the accusations, according to the paper, calling the sex toys purchase "high jinks".
The investment minister was the most senior of several British politicians named in media reports at the weekend accused of inappropriate behaviour or sexual harassment.
They are in the spotlight following the avalanche of harassment and rape allegations against disgraced Hollywood movie mogul Harvey Weinstein.
Former Conservative party cabinet minister Stephen Crabb, a devout Christian, apologised on Saturday after a newspaper investigation found he had sent sexually explicit messages to a young female job applicant.
Hunt said Prime Minister Theresa May would write to the House of Commons speaker -- a lawmaker who acts as its impartial chief officer -- to ask for advice on how to change the culture at Westminster.
"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," Hunt said.
On Friday Jeremy Corbyn, the leader of the opposition Labour Party, called for an end to the "warped and degrading culture" at Westminster.
"The problem doesn't stop with those who make unwanted advances on women, it extends to a culture that has tolerated abuse for far too long," he said.
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