Borno is at the heart of Nigeria's Islamist insurgency for the past 17 years, which has claimed thousands of lives and displaced two million people.
The first blast went off at a post office in the city centre and was immediately followed by another at the popular Monday market nearby, two security sources and three Maiduguri residents told Reuters.
One blast hit the University of Maiduguri Teaching Hospital, and another struck the eastern neighbourhood of Kaleri, all in the early evening of Monday.
"Preliminary investigation reveals that the incidents were carried out by suspected suicide bombers," the state police said in the statement, without saying who was responsible.
Police said normalcy had been restored and security forces had tightened patrols across the city to prevent further attacks, adding that an investigation into the circumstances of the attack was underway.
Security analysts said the attacks had the hallmarks of insurgent group Boko Haram, which together with Islamic State West Africa Province, has been escalating attacks against the Nigerian military in Borno.
Maiduguri is among the safest cities in Borno state but at least five worshippers were killed and 35 others injured on Christmas Eve last year when a suspected suicide bomber detonated an explosive inside a mosque.
Besides the insurgency in the northeast, jihadists have also been expanding in the northwest of Nigeria, where bandit gangs have caused havoc through kidnappings and attacks on communities and schools.
The United States carried out air strikes in Nigeria's northwest in December and has begun deploying a small number of troops to train Nigerian forces confronting militants.
Agencies
