Nigerian troops "intercepted and destroyed" 10 suicide bombers and repelled the attackers, according to PR Nigeria, an agency that disseminates government news.
At least 30 people were killed and the death toll could go higher, the military said.
Maiduguri, the city under attack, is the birthplace of Boko Haram, which emerged as a much more radical entity after Nigerian security forces launched an all-out assault on their compound there, killing 700 people in 2009.
When people gathered, she detonated herself, according to village head Bulama Isa.
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A rocket-propelled grenade exploded, setting alight grass-thatched huts, and a second woman blew herself up, according to Isa. Meanwhile, in Duwari, an outlying suburb of Maiduguri, the village chief, 10 of his children and others were killed, according to residents Ahmed Bala and Umar Ibrahim.
A soldier said the insurgents fired rocket-propelled grenades into four residential areas on the outskirts of the city. Soldiers fired back, and many civilians were caught in the crossfire, according to the soldier, who spoke on condition of anonymity because he is not authorised to speak to journalists.
The nurse, who spoke on condition of anonymity because she is not authorised to speak to reporters, said the hospital was so overflowing with patients that some had to be cared for in the maternity ward.
About 60 people had wounds from bullets and shrapnel from explosive devices, she said. Other wounded people had to be sent to other hospitals in the city.
Among those at Specialist Hospital was a baby found dead, still tied to the back of her mother, after being hit by shrapnel, the nurse said.