"Someone moved the bag to make some space and it just exploded with a loud noise," the witness said.
Navin Ghimire, the home ministry spokesman, said that a little-known Hindu extremist group, the National Defence Army, left a note found at the scene.
The National Defence Army, which says it is fighting to restore the nation's Hindu monarchy abolished in 2008, has previously claimed responsibility for the killing of a missionary in eastern Nepal last July.
"This is the saddest day in the history of Nepali Christians. Never before has there been such an attack on the church in Nepal"
a Christian leader
The group also said it bombed a mosque in the east of the country last year, killing two people.
About 500 people were attending a service at the time of the blast.
Ram Brish Chaudhary told the AFP news agency: "A 15-year old student, Celestina Joseph, and 30-year-old Pabitra Paitri died in the bomb blast. Five of the injured are in serious condition."
"Security has been increased and an investigation is going on."
It was the first such attack on a Christian church in Nepal, where most of the population is Hindu or Buddhist.
"This is the saddest day in the history of Nepali Christians. Never before has there been such an attack on the church in Nepal," Tirtha Thapa, a Christian leader, said.
"We deeply grieve with the families of the dead," he said.
Churches in Nepal hold services on Saturdays because it is a public holiday when schools and offices are closed.