In a speech today, Amanda Spielman is expected to say that the place of smartphones in the classroom is "dubious at best".
The Ofsted chief inspector will also signal her support for schools that take a tough stance on unruly pupils, saying it is "entirely appropriate" for youngsters who misbehave to face punishments such as school community service, writing lines or detention.
She will tell delegates at the Festival of Education at Wellington College, Berkshire: "I fundamentally disagree with those who say that taking a tough stance on behaviour is unfair to children. Quite the opposite, there is nothing kind about letting a few pupils spoil school for everyone else.
"That is why we expect heads to put in place strong policies that support their staff in tackling poor behaviour. And I think it's entirely appropriate to use sanctions, such as writing lines, 'community service' in the school grounds - such as picking up litter, and school detentions. And where they are part of a school's behaviour policy they'll have our full support.
"There's no doubt that technology has made the challenge of low-level disruption even worse, which is why I also support recent calls to back heads who have decided that the way to improve behaviour is to ban mobile phones in their schools.
"I'm not the target audience, but nevertheless I am yet to be convinced of the educational benefits of all-day access to Snapchat and the like; and the place of mobile phones in the classroom seems to me dubious at best."
Ms Spielman's comments come after Culture Secretary Matt Hancock called on heads to ban mobile phones, saying he admired those who do not allow the device to be used during the school day.
In her speech, Ms Spielman will say that pupil behaviour is a key concern of parents, and the first question that they want answered in an Ofsted report.
"I want to see behaviour get the attention it deserves in our inspections, probably through a separate behaviour and attitudes judgement," she will say.
"And when I talk about behaviour, I'm not just talking about serious disruption or bullying, important as these are. I want us to look just as hard at low-level disruption, which stops pupils learning and which can make the job of classroom management miserable."
The Ofsted boss will also say that the watchdog is looking at whether schools are attempting to hide naughty students from inspectors during inspections.
"I want to address once and for all, the constant rumours we hear about badly behaved children being hidden from inspectors, perhaps on conveniently timed school trips.
"My research and analysis teams are currently designing a study to assess the extent of the problem, and what we might do about it."
Malcolm Trobe, deputy general secretary of the Association of School and College Leaders, said: "We can assure the chief inspector that schools do not shy away from putting in place strong behaviour policies and that they are well aware of the importance of a well-ordered and disciplined environment as a cornerstone for effective learning.
"They decide on the nature of sanctions based on their knowledge and experience of what is most effective in their school, and it is important that this remains a matter of professional judgement rather than an expectation that certain sanctions will be used."
He added: "Schools do not allow pupils to use mobile phones during lessons, other than sometimes for specific educational activities. Some headteachers make the decision to allow their use at break time, and some don't. Again, this is a matter of professional judgement on what works best in their context."
Writing in the Daily Telegraph yesterday, Mr Hancock hailed school leaders who do not allow students to have mobile phones during the school day.
"While it is up to individual schools to decide rather than government, I admire head teachers who do not allow mobiles to be used during the school day," he wrote.
A group of Tory MPs has also urged a ban on mobiles during the school day, saying there is evidence it can have "a beneficial effect on pupils' ability to learn".
A Snapchat spokesman said: "Snapchat allows you to express yourself and communicate freely with close friends and family. We think that's a good thing.
"We don't recommend that young people use it all day while at school and, as with any technology, parents and teachers should have regular conversations with young people about the appropriate use of technology."
Snapchat is not intended for children under the age of 13, the spokesman said.
A Department for Education spokeswoman said the Government supported the right of headteachers to use their powers to ban mobile phones.