Residents said that many of the group's fighters fled the city as the bombardment began, some of them disguising themselves by cutting off their hair and beards.
"We spotted dozens of members of Boko Haram fleeing. They stopped by briefly, shaved their hair and beard and discarded their trademark jellabiya [white traditional garments] for t-shirts and jeans, and moved on," Hamad Bulunkutu, a witness, told the AFP news agency.
"They crossed the Gamboru market river and disappeared from there."
Mohamed Yusuf, Boko Haram's leader, was apparently among those who escaped from the compound.
Soldiers were going door-to-door in Maiduguri in an attempt to hunt down Yusuf's followers.
"Security personnel have succeeded in dislodging the militants and I urge everyone to go about their normal duties," Ali Modu Sheriff, the Borno state governor, said on state radio.
"The house-to-house search is still going on and anybody that harbours them will be dealt with according to the law."
Al Jazeera's Yvonne Ndege, reporting from the Nigerian capital, Abuja, said that hundreds of civilians were displaced by the assault on the compound.
"Relief agencies on the ground say at least 1,000 people abandoned their homes ... joining 3,000 others already displaced by the violence," she said.
"There is a huge amount of concern about the humantiarian impact of this fighting. Relief agencies are talking about people not being given access to food and water, and stores running out of basic necessities.
"People are concerned that this violence could lead to total chaos and a state of emergency in some of the northern states of Nigeria."
Abubakar Umar Gada, a senator from Sokoto state in northern Nigeria, told Al Jazeera security agents had been deployed heavily and the situation "is totally under control".
He said Boko Haram had "taken advantage of the large number of people who are unemployed" and lacking opportunities to better their lives.
"We largely have a social problem that has been taken advantage of by these miscreants to cause havoc and confusion," Gada said.
Boko Haram, which means "Western education is prohibited" in the local Hausa dialect, has called for the enforcement of sharia, or Islamic law, across Africa's most populous nation.
Nigeria's 140 million people are nearly evenly divided between Christians, who dominate the south, and the primarily northern-based Muslims.
Islamic law was implemented in 12 northern states after Nigeria returned to civilian rule in 1999 following years of military rule.
The clashes began on Sunday in nearby Bauchi state, with fighters attacking police stations, before spilling over into Yobe.
Residents said fighters armed with machetes, knives, bows and arrows and home-made explosives attacked police buildings and anyone resembling a police officer or government official in the city.
But most of the casualties appear to have been in Maiduguri, the northeastern city known as the birthplace and stronghold of the group.