|Shias are a minority among Nigeria's Muslims|
Security forces killed another five people after arriving at the scene and opening fire, he said.
The military has not commented on the allegation.
No group has said it carried out the attack, but suspicion is bound to fall on militant Sunni Islamist group Boko Haram.
It denounces Shias, a minority in Nigeria, as non-Muslims.
The bomber detonated himself after joining worshippers who were marching to mark Ashura, a solemn day when Shias mourn the martyrdom of Hussein, a grandson of the Prophet Muhammad, in 680 AD at Karbala in modern-day Iraq, witnesses told the BBC Hausa service.
|People at the site of a bomb blast at a bus station in Gombe, |
north-eastern Nigeria - 31 October 2014
Although witnesses reported that 20 people had died in the blast, a Shia representative said the explosion had killed 15 of them and the other five had been shot dead by the security forces, BBC Nigeria correspondent Will Ross reports from the main city, Lagos.
About 50 people are said to have been wounded in the blast.
One man, Mohammed Gana, told Reuters news agency that his brother had been killed in the attack.
He counted 23 bodies at the scene, he said.
Resident Yusuf Abdullahi told Reuters the explosion took place near his home.
"I heard a very heavy explosion as if it happened in my room," he said.
This is not the first time that Shia officials in Nigeria have accused the military of killing their members, our correspondent says.
In July, they accused soldiers in the northern town of Zaria of opening fire on a demonstration, killing three sons of Shia leader Sheikh Ibraheem Zakzaky.
|Sheikh Ibraheem Zakzaky is influential in Shia circles in Nigeria|
He advocates the creation of a Shia-oriented Islamic state in Nigeria, and his supporters have been involved in many clashes with the security forces over the decades.
Boko Haram has waged an insurgency in Nigeria since 2009, with some 2,000 civilians killed this year alone, rights activists say.
It has repeatedly targeted Christians and rival Muslim groups.
In July, it was blamed for bombing an open-air mosque in Potiskum, killing four people.
Potiskum is in Yobe, one of three states where Nigeria's President Goodluck Jonathan imposed a state of emergency in May 2013 after vowing to crush the insurgency. Potiskum town is about 200 km straight west of Maiduguri.
Boko Haram has intensified attacks since then and sparked global outrage in April by abducting more than 219 schoolgirls.
Last week, Boko Haram leader Abubakar Shekau rejected government claims that the two sides had agreed a ceasefire in talks brokered by Chad.
Mr Shekau also denied that Boko Haram planned to release the schoolgirls.
All the girls had converted to Islam, and had been married off, he said.