The northeastern city is a stronghold of Islamist group Boko Haram but it was not immediately clear who was behind the latest violence.
A resident and a doctor at a local hospital reported that gunmen shot dead a married couple and their child as the family left church in Maiduguri's Gwange area.
"We received three bodies of a couple and their child this morning from Gwange with several bullet wounds," said the doctor at the University of Maiduguri Teaching Hospital, who requested anonymity.
"They were brought from Gwange where they were shot by some gunmen as they were leaving a church," he added.
A resident of the Gwange area, Bukar Kolo, told AFP the gunmen fled after the attack outside the Church of Christ in Nigeria building.
Boko Haram have repeatedly attacked Christians attending Sunday worship across northern Nigeria, but there was no indication as to why this family may have been specifically targetted.
Separately, the traditional chief in Gwange, Mala Kaka, who has close ties to the area's top Islamic leader, was gunned down in his home, according to his guards and residents.
"The attackers burst into his sitting room where he was chatting with his friend who visited him and shot them both," a member of his guard said.
"The chief died on the spot while his friend is now in hospital with gunshot wounds."
Resident Abdullahi Faltaye offered a similar account, saying the chief has already been buried.
Kaka was close to the Shehu of Borno state, Umar Garbai el-Kanemi, a key cleric who Boko Haram tried to assassinate in July in a suicide blast in Maiduguri that killed five others but left Kanemi unharmed.
The radical Islamists have vowed to kill many of Nigeria's traditional Muslim leaders, who they accuse of betraying Islam by submitting to the authority of a secular government.
Boko Haram has said it wants to create an Islamic state in the mainly Muslim north of Nigeria, Africa's most populous country, where most people in the south are Christian.
The day of violence in the troubled city also included a blast from an improvised explosive device at 10:15 am (0915 GMT) on a main road that caused no casualties, said Lieutenant Colonel Sagir Musa, spokesman for a joint military taskforce.
A resident identified as Haruna told AFP that a military patrol was the target and that soldiers began indiscriminately firing their weapons after the explosion in Gwange, causing locals to flee.
Earlier this week, residents claimed as many as 30 people were killed during a rampage by soldiers after a bomb attack in the same area. The military denied the accusations.
Boko Haram has repeatedly targeted the security services as part of its insurgency, which has included targetted killings as well as large scale bomb attacks.
The group is blamed for killing more than 1,400 people in Nigeria since 2010. Maiduguri is considered the group's base.
