But some teaching unions and trusts have argued that smartphone devices have now become an essential part of learning.
Mr Gibb said: "Many schools have already taken the decision to ban mobile phones from the classroom.
"While this is clearly a matter for the head teacher, my own view is that schools should ban their pupils from bringing smartphones into school or the classroom.
"Children should not be spending hours and hours on their smartphones or iPads.
"There are obviously huge benefits to the internet and there's nothing intrinsically damaging about spending time online
"But if the time children spend using social media or playing computer games becomes excessive, it drives out time for them to talk to their parents, exercise, do their homework or play with friends.
"It eats into the amount of sleep and rest children have, resulting in their coming into school the next day tired and unable to concentrate."
But Patsy Kane, executive head teacher at the Education and Leadership Trust in Manchester, said mobile phones and devices have become brilliant learning tools and students should be encouraged to used them.
She said: "There's a fantastic range of apps now for revision - and the students are really motivated to use them.".
And Sarah Hannafin, from the National Association of Head Teachers, added: "Mobile phone bans certainly work for some schools but there isn't one policy that will work for all schools.
"Outright banning mobile phones can cause more problems than it solves."