His office said that protesters had started the fire.
People watched from a nearby street and fire trucks were at the scene.
Local TV broadcast drone footage of huge crowds of protesters filling the streets of Colombo around the Presidential Secretariat building.
Sri Lanka's parliamentary speaker announced on Saturday that President Gotabaya Rajapaksa plans to step down, bowing to intense pressure after a violent day of protests in which demonstrators also stormed the president's official residence.
Neither Rajapaksa nor Wickremesinghe were in their residences when the buildings were attacked.
Speaker Mahinda Yapa Abeywardena said in a video statement that Rajapaksa had informed him that he would step down from his post next Wednesday.
Wickremesinghe also said he was willing to resign to make way for an all-party government, his office said in a statement on Saturday evening.
Throughout the day, soldiers and police were unable to hold back a crowd of chanting protesters demanding Rajapaksa's resignation and blaming him for the country's worst economic crisis in seven decades.
At least 39 people, including two police officers, were injured and hospitalised during the protests, hospital sources told Reuters.
The country is struggling under a severe foreign exchange shortage that has limited essential imports of fuel, food and medicine, plunging it into the worst economic crisis since independence in 1948.