In a decree, Noboa said the move aims to "get closer to the people and address their needs on the ground."
Vice President Maria Jose Pinto was instructed to temporarily perform her duties from Otavalo, a city in northern Imbabura province, Xinhua reported.
The announcement came a day after the government suspended diesel subsidies, triggering opposition from transport unions, indigenous groups and labor organizations.
On Saturday, urban transport operators in Pichincha province -- home to Quito and the executive's official seat -- announced they would halt services starting on Monday.
The subsidy removal increased diesel prices from 1.80 to 2.80 US dollars per gallon, effective Saturday.