Eight vigilantes were killed in the first blast in the Igwanda area of the city at about 12:15 pm while two died in the second outside a pub and brothel in the Dorawa area.
There was no immediate claim of responsibility but Potiskum has been hit repeatedly by Boko Haram in its six-year insurgency, including by suicide bombers.
The first attack targeted the civilian vigilante office in the Igwanda area of the city and came after a man seen carrying laptops and other computer accessories was detained.
“We suspected he was a thief and then when he couldn’t explain how he came about the things that were found on him, we took him to our office for interrogation,” said one vigilante group member.
“But we didn’t know he had explosives on him. He detonated the explosives and we lost eight men, including our commander,” said the vigilante, who asked not to be named for his own safety.
Yobe Police Public Relations Officer (PPRO), Toyin Gbadegeshin, also confirmed the explosions.
He identified the vigilante leader killed as Ado Kwamanda.
“Two people, including the bomber, died in the second attack,” he said.