The state of emergency came into effect on April 1, according to an official gazette issued Friday, and allows authorities to arrest and imprison suspects without warrants.
Rajapaksa said the decision to impose the state of emergency was made in the "interests of public security, the protection of public order and the maintenance of supplies and services essential to the life of the community."
The island nation of 22 million people is struggling with an ongoing economic crisis that has seen people forced to queue for basic goods and face hours-long power blackouts.
The declaration follows violent protests Thursday night, which saw furious demonstrators hurl bricks and set fire to a bus outside the President's private residence in the capital, Colombo, Reuters reported.
Police used tear gas and water cannons to break up the protests, according to Reuters, as officers arrested dozens of people and imposed a curfew in parts of Colombo overnight, C. D. Wickramaratne, the inspector general of police, said in a statement.
President Rajapaksa's office released a statement Friday alleging that "organized extremists" wielding iron rods, clubs and poles incited protesters to "riot" outside his residence.
Later on Friday, Sri Lanka's minister for community police services, Dilum Amunugama, called the protest an act of terrorism.
"I think the wrong terminology was used in the official communique. These were not extremists, they were terrorists," he told reporters. "The government stance is that if terrorism prevails, it should be defeated."
"The main issue Sri Lanka is facing is a forex shortage and protests of this nature will hurt tourism and have economic consequences," Ranatunge said.
What's happening in Sri Lanka
Sri Lanka is battling a foreign exchange crisis that forced a currency devaluation and has impacted the supply of basic goods such a food, medicine and fuel.
Demonstrators have held peaceful protests over the situation for weeks, with some calling on the President to resign, but Thursday's protests mark an escalation in the crisis.
Hanaa Singer-Hamdy, the resident coordinator for United Nations Sri Lanka, called for restraint from all groups.
Journalist Rukshana Rizwie reported from Colombo, Sri Lanka. CNN's Alex Stambaugh and Sophie Jeong reported from Hong Kong. Additional reporting by Reuters.