The bombing -- claimed by the Islamic State group -- follows what has already been a bloody month with the Taliban ramping up assaults on security forces across the country and IS targeting the capital Kabul, with hundreds killed according to estimates.
The attack appeared to target a protest camp outside an election commission office where a group of people were rallying in support of a candidate disqualified from parliamentary elections due in October.
Jalalabad is the capital of Nangarhar province, the main IS stronghold in Afghanistan.
The blast "killed two people, and four others were wounded", provincial governor spokesman Attaullah Khogyani told AFP, adding that it was carried out by a suicide attacker.
Provincial health director Najib Kamawal confirmed the two deaths.
An eyewitness to the bloody aftermath of the attack said a suicide bomber detonated near a tent full of protesters outside the office, and that security forces had cordoned off the area.
"It was very big blast and it shook our home," said witness Mirza Amin, who added he lived 50 metres (160 feet) from the site of the explosion.
Earlier this month, Afghanistan's Independent Electoral Complaints Commission disqualified 35 candidates from running in the upcoming parliamentary election for having direct links to illegal armed groups.
The protest in Jalalabad was against the disqualification of candidate Javed Zaman Ghamsharik, who was barred for allegedly possessing illegal arms and for connections to illicit land deals.
The blast comes nearly a week after President Ashraf Ghani offered a conditional three-month ceasefire to the Taliban, a move welcomed by the United States and NATO after nearly 17 years of war.
The Taliban have yet to officially respond to the offer.
The surge in violence this month comes after Afghans marked an unprecedented nationwide ceasefire between the Taliban and government forces in June, giving some relief to war-weary civilians.
For three days, thousands of insurgents poured into cities across Afghanistan, eating ice cream and taking celebratory selfies with security forces.
The brief respite spurred hopes a new path was opening for peace talks in the country after nearly 17 years of war.
The Taliban have long insisted on direct talks with Washington and refused to negotiate with the Afghan government, which they see as illegitimate.
Earlier this week, Gen. John Nicholson -- the top commander for US and NATO forces in Afghanistan -- said that warring parties now have an "unprecedented" opportunity for peace, citing the June ceasefire as a step forward.
He stressed, however, that any peace talks must ultimately be "Afghan-led, Afghan-owned".