Around 30 gunmen took part in the assault on the Jalalabad jail overnight, using a car bomb to blast the building’s entrance before storming the jail.
A series of explosions were then heard as gunmen shot at prison security guards.
Hundreds of prisoners attempted to flee the prison, which holds some 2,000 inmates including a large number of Taliban and Isis prisoners.
Three Isis fighters and at least 21 others were killed in the battle, while 43 were injured, Attaullah Khygyani, a spokesperson for the governor of Nangarhar province said on Monday.
The dead include civilians, prisoners, guards and security personnel, Mr Khygyani added. Afghan officials have warned the death toll may rise.
The battle continued into Monday, with gun shots being heard from the prison area, Mr Khygyani said.
The police had captured around 1,000 escaped detainees by midday on Monday, lawmaker Sohrab Qaderi said. It is not known how many prisoners remain at large, but police suspect some are hiding in a neighbouring housing complex.
Civilians were evacuated from the area surrounding the prison as special forces arrived at the scene to reinforce police efforts.
The attack comes a day after the Afghan intelligence agency killed a senior Isis commander near Jalalabad.
Meanwhile, Jalalabad, which is 130 kilometres (80 miles) east of Kabul, remains under lockdown due to the coronavirus.
“The whole city of Jalalabad is under curfew, shops are closed,” Mr Qaderi said. “Jalalabad is completely empty.”
The Taliban was not involved in the attack, their political spokesperson has said. “We have a cease-fire and are not involved in any of these attacks anywhere in the country.”
The militant organisation declared a three-day ceasefire from Friday to Monday for Eid al-Adha.
There are around 2,200 Isis followers in Afghanistan, the United Nations estimated last month.
In the same report, the UN found that the militant group “remains capable of carrying out high-profile attacks in various parts of the country, including Kabul”, despite being in territorial retreat with a diminished leadership.
Another report by the intergovernmental organisation found nearly 1,300 civilians, including hundreds of children were killed during the first six months of 2020, representing a 13 per cent fall on the same period the previous year.