Ministers want all pupils in England to study maths, English, science, one of history or geography and a modern language at GCSE.
But some young people "will find it a problem" Sir Michael Wilshaw, told the Times Educational Supplement (TES).
Sir Michael said vocational subjects would suit some pupils better.
In particular he questioned whether the academic subjects included in the government's Ebacc would be the best thing for pupils who wanted to take apprenticeships when they left school.
"I can think of youngsters, even at the highest-performing schools, who will find it a problem and who would have been better suited to do English, maths and science and a range of vocational subjects," he told the magazine.
In June, the Education Secretary Nicky Morgan confirmed she wants all pupils to have to study the five traditional subjects included in the Ebacc school performance measure.
According to Mrs Morgan the move would ensure all pupils received a rigorous academic education and avoid pupils from disadvantaged backgrounds being put off academic subjects.
In addition, the Conservative manifesto pledges that schools which do not have 100% of pupils studying this set of subjects at GCSE should not be able to obtain Ofsted's top rating of "outstanding".
Both policies will be subject to a government consultation later in the autumn.
Sir Michael told the TES he agreed more young people should be studying these subjects - but said the combination was not suitable for everyone.
The Association of School and College Leaders, which represents secondary heads, welcomed Sir Michael's challenge to government policy.
General Secretary Brian Lightman said the union shared his concerns.
He said a recent survey by the union found almost 90% of school leaders disagreed with making these subjects compulsory for all pupils.
"It is unfair on young people to take a one-size-fits-all approach to their education.
"We are concerned that creative, technology and vocational subjects will be squeezed out of the curriculum."
Mr Lightman said the union would urge ministers to make the choice of GCSE subjects more flexible.
The Department for Education said an additional league table measure, Progress 8, allows pupils to study a wider range of subjects.
"As part of Progress 8, pupils will be able to study up to three of our new gold-standard Tech Awards which will provide a real foundation for progression on to vocational courses including apprenticeships," said a spokesman.

Three others were injured, one seriously, in the incident at Downsview Park, medical officials said.
The collapse happened an hour before the gates were due to open for the concert, with queues already beginning to form outside.
UK rock band Radiohead tweeted that the performance had been cancelled due to "unforeseen circumstances".
Emergency crews went to the scene and the area was evacuated.
Toronto police said the stage collapsed at 16:00 local time (20:00).
Police said the person who died was a man in his 30s, but did not reveal his identity.
The victims were all part of a team involved with setting up the stage, officials said.
Alexandra Halbert, who was working in a beer tent at the show, said she was about 200-300 yards away from the stage, with her back to it, when she heard "something that sounded like fireworks".
"I turned around and the whole top part of the stage had collapsed, as well as the scaffolding," she told the BBC.
"It seemed like there were a couple of minutes of hesitation and no one knew quite what to do. It was only afterwards that we all realised how serious it was."
Jason Ip, a food vendor, said there was "chaos" as people waited for the emergency services to arrive.
"A few people started running towards the stage. No one knew exactly what had happened, but it was clear that people were underneath the stage," he said.
"It was like witnessing a car accident. In a situation like that, you just aren't sure how to react."
Some 40,000 people were expected for the sold-out gig, which was also due to feature Canadian musician Caribou.
A key government policy to force all pupils to sit GCSEs in core academic subjects could be difficult for some students, the head of Ofsted has said.
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One person has died in a stage collapse before a Radiohead concert in the Canadian city of Toronto.