Witnesses said the bombs hit several targets, including churches and the headquarters of the Yobe state police.
Boko Haram told a newspaper it was behind the attack and that it planned to hit further government targets.
The death toll is expected to rise with some reports claiming at least 150 people dead.
President Goodluck Jonathan was “greatly disturbed” by the attack, and said his government was working hard to bring those “determined to derail peace and stability in the country to book”, according to a spokesman.
Witnesses said the attacks began on Friday at about 18:30 and lasted for about 90 minutes. Gunmen then engaged in running battles with security forces.
A Roman Catholic parish priest told our correspondent his church had been burnt down and eight other churches also attacked.
He described gangs of young men roaming the streets throwing improvised bombs into the churches.
Boko Haram, which means “Western education is forbidden”, has launched frequent attacks on the police and government officials.
The attacks followed a triple suicide bomb attack on a military headquarters in Maiduguri, in neighbouring Borno state.
Military officials said the three attackers had died. Officials really are geniuses. Most people carrying out a suicide bomb attack tend to die. The sad part is they take many innocent people with them.
Newswarped knows these friggin suicide turnips will never see paradise.