"The explosions were caused by IEDs in different parts of the city and as groups of people were celebrating independence day," the Nangarhar governor's spokesman Attaullah Khogyani said, referring to improvised explosive devices.
Jalalabad is the scene of frequent bomb attacks, and the surrounding terrain is home to both Taliban fighters and the Islamic State group's local affiliate.
At least 52 people were wounded, Khogyani said. Zaher Adel, a spokesman for a local hospital, said 66 wounded people had been brought in. An AFP correspondent saw children among the victims.
This year's August 19 celebrations mark 100 years of Afghan independence from British influence.
The day was supposed to be one of national pride and unity, but was overshadowed by an IS suicide attack Saturday on a crowded Kabul wedding hall that killed at least 63 people. In Kabul, locals took to the streets to wave the black-red-and-green Afghan flag, but several public events to commemorate the date were scrapped as Kabul mourns and due to fears of a fresh attack. "We postponed the celebrations to honour the victims, but we will definitely take revenge for our people," Afghan President Ashraf Ghani said.