CRS director of communications Kim Pozniak said on Monday that the incident occurred in the town of Kobo, where residents reported heavy artillery fire on Sunday, but did not say whether the shootings were linked to the unrest.
The victims were Chuol Tongyik, one of CRS's security managers, and Amare Kindeya, a driver. They were returning from Amhara to the capital Addis Ababa, the statement said.
"The depth of our shock and sorrow is difficult to measure and we are saddened over this senseless violence," Zemede Zewdie, CRS's country representative in Ethiopia said in the statement.
"Details of the murder are still unknown," CRS said in a statement.
Spokespeople for Ethiopia's federal government and for the Amhara regional government did not immediately respond to requests for comment.
Thousands have protested across Amhara since the federal government issued its order on Thursday and residents reported gunfire in at least two towns on Sunday.
Residents in the town of Dessie reported large protests there on Monday, with young people blocking the roads and burning tires.
Amhara politicians and activists have condemned the government order that requires special forces from each of Ethiopia's 11 regions - which enjoy a degree of autonomy - to integrate into the police or the federal army.
They say disbanding Amhara's special forces would leave the region vulnerable to attacks by neighboring regions, including Tigray, whose leaders agreed a truce with the federal government in November to end a two-year war that killed tens of thousands.