Asked about the incident while on a trip to Brussels, Prime Minister Sir Keir Starmer said his first thoughts "as a father" were with the victim's family.
"The terrible stabbing in Sheffield is one where I think the whole country would want to reach out to the family, to the friends, to the school, the entire community in their grief and mourn with them," he said.
Louise Haigh, the MP for Sheffield Heeley, said the news was "horrific" and her thoughts were with all affected.
"Serious questions will have to be answered about how this could have happened", she said, adding she will work with the school, police and the council "to make sure they are".
Education Secretary Bridget Phillipson said she was "devastated" by the boy's death.
She added: "We are in contact with the school and council to offer support."
In an emotional statement education minister Catherine McKinnell told the Commons: "My heart goes out to his family, friends and the entire school community at this very distressing time."
South Yorkshire Mayor Oliver Coppard said he had spoken with Lauren Poultney, the county's chief constable, and offered her his full support.
"This morning a teenage boy went to school like thousands of others across South Yorkshire but won't come home; a young man who was a member of our community, with his whole life ahead of him," he said.