A woman and her two children were among the victims of the attack at the Redeemed Christian Church of God, the sources said.
Though no one has claimed responsibility for Sunday's attack, the method, target and location are consistent with past attacks thought to be perpetrated by the militant Islamist group Boko Haram
Potiskum, the commercial hub of Yobe state, has been the site of multiple deadly attacks blamed on the group.
In 2015, militants have targeted Potiskum on at least four occasions, police said: In January, three people were killed and 43 were injured
when two female suicide bombers targeted the mobile phone market; the following week, another suicide attack killed four people and injured 48
at a bus station in Potiskum. Another suicide attack at a bus station in February
killed 17 people and injured 27; and in May, a gunman wearing a suicide vest
attacked the College of Administrative and Business Studies there.
In addition to schools and police and government buildings, Boko Haram has been known to target churches, as evidenced by a rash of church attacks in June 2013 that left more than 50 people dead and a November 2011 string of attacks that included assaults on 11 churches.
The United States condemned recent attacks by Boko Haram in northeastern Nigeria.
"As we have said before, the people of northern Nigeria deserve to live free from violence and from terror. The United States continues to provide counterterrorism assistance to help Nigerian authorities develop a comprehensive approach to combat the threat posed by Boko Haram," U.S. State Department spokesman John Kirby said in a statement.
Separately on Sunday, deadly blasts rocked the central city of Jos.
One blast happened near the Yan-Taya mosque as a sermon on the occasion of the Muslim holy month of Ramadan was underway.
Another blast happened at Bauchi Road, a major thoroughfare in Jos that is also in an area where many Muslim families reside.
According to a source at Plateau Hospital in Jos, at least 15 people were killed and 20 others were injured in the attacks.
The city of Jos in central Nigeria sits between the predominantly Christian and animist southern half of the country, and northern Nigeria, where the majority of the country's Muslims reside.