Downing Street has publicly rebuked the foreign secretary for accusing UK ally Saudi Arabia of engaging in "proxy wars" in the Middle East.
Number 10 said his views did not represent "the government's position".
Sir Malcolm Rifkind, a former Conservative foreign secretary, said "the jury is out" on Mr Johnson's future in the job.
He told BBC Radio 4's Today programme Mr Johnson was not entitled to make public statements which are "completely at variance with what the government line is", and the prime minister was right to slap him down.
Sir Malcolm said: "If he wants to be foreign secretary for the foreseeable future - and he could be a very good one, he's a highly intelligent guy... it's the question of his temperament".
Mr Johnson is to deliver a keynote speech at a major regional conference in Bahrain on Friday before heading to Saudi Arabia on Sunday.
Theresa May's official spokeswoman said the prime minister had "full confidence" in Mr Johnson but that his comments at a conference in Italy were his own personal view.
She added that Mr Johnson will have the opportunity to set out official policy - of Britain's desire to strengthen its ties with Saudi Arabia and support for its controversial military involvement in Yemen - when he travels to the desert kingdom.
Sir Malcolm said: "He's often been in this situation before, and he's got a remarkable use of language."
However, if Mr Johnson persists in offering his personal view in public, Sir Malcolm said: "I think inevitably the prime minister would say - look is his role adding to the benefits for the United Kingdom".
"He might end up being more comfortable in another senior cabinet position".
Mr Johnson's comments were made at a conference last week but only emerged after the The Guardian newspaper published footage of the event.
In it the foreign secretary said: "There are politicians who are twisting and abusing religion and different strains of the same religion in order to further their own political objectives.
"That's one of the biggest political problems in the whole region. And the tragedy for me - and that's why you have these proxy wars being fought the whole time in that area - is that there is not strong enough leadership in the countries themselves."
In defence of Mr Johnson, Tory colleague and housing minister Gavin Barwell said: "It's his job to set out the concerns that we have."
He told the Daily Telegraph newspaper that Saudi Arabia was a "friend" but he added: "Many of our constituents have concerns and it's quite right that we should raise them."
Meanwhile, Tory backbencher Sarah Wollaston tweeted: "Boris was speaking the truth on proxy wars and it's time for all parties in the region to end the sectarian bloodbath.
"To proxy wars charge I'd add beheadings, judicial mutilations, torture, violation of women's human rights through male guardianship, unfair trials, gross restrictions on free speech, rights of assembly and association, bombing civilians in Yemen."
Mr Johnson's speech at the International Institute for Strategic Studies (IISS) Manama Dialogue event in Bahrain will be closely watched at home and abroad.
Dr John Chipman, director-general and chief executive of the IISS, said: "Each year, with this regional security summit, we take the temperature, measure the pulse, and analyse the direction of change in the Middle East.
"I am delighted that Boris Johnson has agreed to give the keynote speech and we expect delegates to be keenly interested in his views on the region and on UK strategy towards it."
Sir Malcolm, who was foreign secretary between 1995 and 1997, said that Mr Johnson has made an "extraordinary impact" as a celebrity, but he warned: "As a foreign secretary you can't be a celebrity."
"Harold MacMillan was once foreign secretary, and in his memoirs he said: 'Foreign Ministers are either dull or dangerous'. Well Boris certainly isn't dull."
Boris Johnson is to begin a tour of the Middle East amid a row over comments he made about Saudi Arabia.