The MP for Braintree, who was first elected in 2015, concluded that he was "highly unlikely" to reach the final two candidates chosen by MPs to be put to a final vote of Tory members.
Mr Malthouse announced he would withdraw on Tuesday.
His withdrawal leaves 11 runners still in the contest to replace Theresa May, who will quit as Tory leader on Friday.
Mr Cleverly said: "I felt that we needed to deliver Brexit and then quickly move the conversation on to other important issues that face the country.
"I had hoped that the Conservative parliamentary party would support me to be the face and voice of that conversation.
"To do this I asked them to make a leap of faith, skip a generation and vote for a relatively new MP.
"It is clear that, despite much support, particularly from our party's grassroots, MPs weren't comfortable with such a move and it has become clear that it is highly unlikely that I would progress to be one of the final two candidates."
In a statement posted on Twitter Mr Malthouse said: "After 20 years in front line politics as a councillor, Deputy Mayor, MP and Minister, I wanted to lead a new generation of Conservatives stepping forward at a time of profound change in our country.
"But that experience has also made me a realist and the last few days have demonstrated that there is an appetite for this contest to be over quickly and for the nation to have a new leader in place as soon as possible.
"As such, it seems right to me that I withdraw my candidature and wish those remaining the very best, always recognising there are going to be very challenging times ahead."
Read more from Yahoo News UK
On Tuesday afternoon the 1922 Committee revealed candidates will need a proposer, seconder and six other MPs to formally stand.
To pass through the first ballot they need to win 5% of the vote - or 17 MPs - while the second round increases to 10%, the equivalent of 33 MPs.
Under these proposals Matt Hancock - currently endorsed by 11 MPs may not make the second round ballot.
Security Minister Mr Wallace ran Mr Johnson's leadership campaign in 2016 and threatened to go "Game Of Thrones" on Mr Gove after he scuppered his candidate's chances, opening the door for Mrs May's coronation.
Mr Wallace would only say that he had not yet decided whether to back Mr Johnson when asked directly on BBC Radio 4's Today programme.
He said: "I haven't made a decision yet.
"The one thing I have learned from being inside a campaign is we've got another 10 days - your listeners will be dead bored.
"What we do need to do is make sure this race is about getting the right person to lead the country, but I'm not going to bang on about it."
Meanwhile, International Trade Secretary Mr Fox announced he is backing Mr Hunt because he wants to steer away from a no-deal Brexit.