“Clinical trial results show that the vaccine is safe and effective in this age group,” it said in a statement.
The Comirnaty vaccine is administered in two doses of ten microgrammes three weeks apart.
An ongoing clinical trial of more than 1,500 people “shows that the Covid-19 vaccine offers almost complete protection against serious illness caused by the SARS-CoV-2 virus in 5 to 11-year-olds”, it said.
“Side effects tended to occur less frequently than in adolescents or adults. They included pain at the injection site and tiredness, or less frequently headache, aching limbs or fever,” the agency added.
The vaccinations had been until now limited to children aged 12 or older.
Switzerland is currently experiencing a strong fifth wave of the virus.
Only the Comirnaty and Moderna vaccine are authorised in Switzerland.
The country joins Portugal, Italy, Greece and Spain in Europe in giving the green light to the vaccination of children in this age group.
Canada and the United States as well as Israel and Chile have also authorised the vaccination of children of a similar age.
In France, vaccination has only been approved for young children at risk of developing serious illness but the government has said it is considering extending it to all children on a voluntary basis.