The Tonbridge & Malling MP had made it to the last five candidates by securing the requisite votes last week to make it through to Monday night’s ballot.
But Mr Tugendhat, who was standing to replace Boris Johnson after the PM said he would step down earlier this month, received just 31 votes out of more than 350 MPs on Monday (July 18), which relegated him out of the competition.
The vote was held after a series of private hustings in front of MPs and the 1922 Committee.
The MP who has never held ministerial office but chairs the Commons Foreign Affairs Committee, had promised the UK a ‘clean start’.
The former army officer, who had served in Afghanistan and Iraq, also pledged to spend three per cent of gross domestic product (GDP) on defence and security.
Former Chancellor Rishi Sunak received the most votes on Monday with 115, followed by Penny Mordaunt with 82, Liz Truss with 71 and Kemi Badenoch with 58, and all of which remained in the leadership race.
A further round of voting is to take place on Tuesday when another candidate will be ejected from the leadership race.
A subsequent round is set to take place later this week to leave just two candidates who will then battle it out over the summer to win the support of Conservative members, with their choice of the next prime minister being unveiled on September 5.
Mr Johnson will then formally tender his resignation to the Queen to make way for his successor the following day.