They failed to gather sufficient support from fellow Tory MPs.
Despite his win, Mr Johnson lay low on Thursday and did not appear on camera to speak about it.
When approached by ITV News for a comment at a dinner on Thursday evening, Mr Johnson did not respond to questioning.
Shortly after the results of the ballot were announced, the former foreign secretary took to Twitter instead to tweet his thanks but warned "we have a long way to go".
ITV News Political Editor Robert Peston says Mr Johnson's place in the final two is all but assured as he would have to lose support before next week's second ballot.
Grassroots members of the Conservative party in Cheshire have been reacting as the first set of votes came in. Among those watching were voters in Crewe, a railway town at the gateway to the North West. They hope a new leader would seek to close the North-South divide.
There was mixed reaction to the still-standing contenders, with not all favouring Boris Johnson for the top job.
Rebecca Barry has been the meet Conservative party members before they vote.
Meanwhile, Foreign Secretary Jeremy Hunt, who is one of the favourites, tweeted he was pleased to have come second in the first round of voting.
Amber Rudd, his Cabinet colleague and one of his more high-profile backers, said it was important to realise this contest was not about catching Boris Johnson but about getting through to the final two where the views of the party faithful, the membership, would hold sway.
"The important thing is to come second, and that's exactly what Jeremy did," she told ITV News.
Rival Rory Stewart, the International Development Secretary, told ITV News he was delighted to make the cut - and insisted he would not bow to pressure to step aside before next week's second ballot.
"I went on an very unconventional campaign where I've been engaging with members of the public, it was a huge risk," he said.
"Boris is a phenomenally difficult person to beat - but I'm the only candidate in the race with a chance to beat him," he said.
Priti Patel, a Johnson supporter, said the race should be allowed run to its course and it should not end up a "coronation".
The full breakdown of the first ballot was (in alphabetical order):
Michael Gove 37
Matt Hancock 20
Mark Harper 10
Jeremy Hunt 43
Sajid Javid 23
Boris Johnson 114
Andrea Leadsom 11
Esther McVey 9
Dominic Raab 27
Rory Stewart 19
Tory MPs had cast their secret vote in a committee room in the House of Commons for who they'd like to see lead the party - and become the next prime minister.
There were 313 votes cast.
Former Brexit secretary Dominic Raab, who received 27 votes, said: "This campaign is just getting started and we've got a good base to build on.
"I'm the change candidate who can be trusted to deliver Brexit by October and has the vision and energy to take Britain forward, and beat Jeremy Corbyn."
He later said that he recognised he was the underdog but was relishing the chance to put forward his case in the first televised live leadership debates, due to be held on Sunday.
In a video posted on Twitter, Michael Gove said it was "all to play for".
The environment secretary - who infamously pulled his support for Mr Johnson at the last minute during the last leadership race - said: "I now want to make sure that we have a proper debate about ideas.
"I believe that I've got the policies that can transform this country for the better."
Defeated ex-work and pensions secretary Ms McVey said she had yet to make up her mind on who to support after gaining the least support in the first round.
“I am pleased to have had a platform to make the case for Blue Collar Conservatism, a clean break from the EU and the need to invest money into schools, policing and a proper pay rise for our public sector workers," she said.
“I will speak to the remaining candidates to see who is best placed to deliver on that programme."
Leadership hopefuls needed at least 17 votes in the secret ballot to go through to the second round, with anyone below the threshold automatically eliminated.
Former Commons leader Andrea Leadsom had earlier insisted she was “very optimistic” about the ballot.
Speaking on Thursday morning she said she was "definitely" not going to pull out and would not be drawn on who she would support if she didn't make it through to the final two.
Prime Minister Theresa May refused to say who she voted for.
"That's none of your business," she joked as she left the committee room in the Commons where the ballot is being held.
Former chief whip Mark Harper had spoken of his confidence about making the cut but his chances were written off by Jacob Rees-Mogg, who is backing Johnson.
Mr Rees-Mogg said: "Mark Harper doesn't seem in a very strong position.
"The bottom one goes and anyone under 5% goes. So, it could be more than one who's knocked out."
Meanwhile, Labour said it would continue to fight to prevent a no-deal Brexit after the latest cross-party attempt by MPs to take control of Commons business was narrowly voted down.