Hospital sources said that nine foreigners were among those killed in the blasts while 13 others have been injured.
In a special statement, the police urged the public to stay indoors and not gather at the explosion sites which had been sealed off.
Television footage showed ambulances rushing the injured to the Colombo National Hospital, the Batticaloa Hospital in the east and the Negombo Hospital on the outskirts of the capital where the explosions took place.
The government said that an urgent security council meeting was underway, with the participation of Prime Minister Ranil Wickremesinghe.
Both President Maithripala Sirisena and Prime Minister Ranil Wickremesinghe have condemned the attacks and appealed for calm.
According to Police, three churches and three hotels have been targeted in the blasts and security has been beefed up across the country.
There has been no claim of responsibility so far for the multiple blasts.