According to army and police sources, 14 people were wounded in the blasts, one of which was caused by a suicide car bomb in the centre of Baquba, capital of Diyala province, north of Baghdad.
Two car bombs also went off near on the northern outskirts of the city and another in the parking lot of the army's 5th division headquarters on the eastern edge of town.
Three bombs were discovered on the main street of Baquba and detonated in a controlled manner by the security forces.
"This is an attempt to destabilise the province," Bakr al-Tamimi, a lieutenant colonel in military intelligence based in Baquba, said.
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"The total number of wounded is 14, the damage was mostly material," he said, adding that all of the blasts occurred at around the same time early in the morning.
He said the attacks were an attempt by the Islamic State group to stretch the security forces battling them on other fronts, including in Baiji refinery and in the Hamrin mountains straddling the provinces of Salaheddin and Diyala.
A senior security official who spoke on condition of anonymity said intelligence had been received of imminent attacks.
"The information we had before this morning is that 74 car bombs were ready to target Diyala," he said.
"Measures were taken today to close the main entrances to Baquba... The road between Baghdad and Diyala is indefinitely closed. Inside the city however, movement is normal," he said.
Sporadic violence has continued to plague the ethnically and religiously mixed province of Diyala since IS lost its last fixed positions there in January.