The attack is the first suicide assault since campaigning officially kicked off last Friday for the parliamentary elections, preparations for which have already been marred by bloody violence.
More than 40 people were wounded when the militant blew himself up among supporters of candidate Abdul Nasir Mohmmand in the Kama district of the eastern province of Nangarhar, provincial governor spokesman Ataullah Khogyani said.
Mohmmand was alive, Khogyani confirmed, but he did not say if the candidate had been hurt in the blast.
Provincial health director Najibullah Kamawal put the death toll slightly higher at 14.
Some of the wounded were in a critical condition, he said.
An AFP reporter saw numerous ambulances delivering bodies and wounded people to a hospital in the provincial capital of Jalalabad.
Sayed Humayun, who had brought his injured cousin to the medical facility, said scores of people had been inside a hall listening to Mohmmand speak when the bomber struck.
"I heard a big explosion," Humayun told AFP.
"For a while I could not see, I thought I was blinded, but later I saw I was surrounded by bodies and people covered in blood." The force of the blast caused the ceiling to collapse on top of the gathering.
"There are still people trapped under the rubble," Malik Zeerak, who was at the rally, told AFP.
No group immediately claimed the attack, but the Islamic State group has taken responsibility for most of the suicide bombings in recent months.
Violence has plagued the run-up to Afghanistan's long-delayed parliamentary vote, which is scheduled for October 20.
Five candidates have been murdered in targeted killings, according to the Independent Election Commission, and there are fears violence will escalate.
There were also numerous attacks on voter registration centres, including a suicide blast at a centre in Kabul that killed dozens.
The latest attack comes amid predictions for Afghan battle deaths to top 20,000 this year -- including civilians and combatants.
That would be the highest number since the start of the conflict in 2001 and make Afghanistan deadlier than Syria.
More than 2,500 candidates will contest the vote, which is seen as a test run for next year's presidential election.
But preparations have been in turmoil for months.
Bureaucratic inefficiency, allegations of industrial-scale fraud and an eleventh-hour pledge for biometric verification of voters threaten to derail the election and any hope of a credible result.
The international community is pushing hard for the vote to happen before November's ministerial meeting in Geneva, which the United Nations says is a "crucial moment" for the Afghan government and its foreign partners to demonstrate progress.
Some 54,000 members of Afghanistan's beleaguered security forces will be responsible for protecting more than 5,000 polling centres on election day.
More than 2,000 polling centres that were supposed to open will be closed for security reasons.
It is a daunting task as the Taliban and IS, which have vowed to disrupt the ballot, ramp up attacks across the country.