The majority died while trying to flee the Pedrógão Grande area, 50 km (30 miles) south-east of Coimbra, in their cars, according to the government.
Several fire fighters are reported to be among about 20 people injured.
"Unfortunately this seems to be the greatest tragedy we have seen in recent years in terms of forest fires," said Prime Minister Antonio Costa.
The death toll could rise further, he said.
Secretary of State for the Interior Jorge Gomes earlier said that three people died from smoke inhalation and 16 died in their cars on the road linking Figueiró dos Vinhos to Castanheira de Pera.
About 60 forest fires broke out across the country overnight, with 1,700 firefighters working to put them out.
The flames spread "with great violence" on four fronts, Mr Gomes said.
Spain has sent two water-bombing planes to help tackle the fires.
It is not yet known what caused the fire, which has also burnt down houses in the area.
However Mr Costa said dry thunderstorms could have been one possible cause.
Portugal has been experiencing a heatwave, with temperatures over 40 C in some areas.
The death toll in forest fires in Portugal has risen to 25, officials say.