In Hilla, about 80 kilometres (50 miles) south of the capital, a police officer said the Ammar bin Yasser mosque in Bakerli neighborhood was bombed after midnight.
"After we heard the explosion, we went to its source and found that IEDs (improvised explosive devices) had been planted in the mosque," the captain said.
"Residents said a group of people with military uniforms carried out this operation," he said, adding that 10 houses were also damaged by the explosion.
The Al-Fateh mosque in a village called Sinjar, just outside Hilla, was also damaged in similar circumstances, AFP reported. The police captain said three or four men in military uniforms were involved that bombing.
"They took advantage of the cold weather, there was nobody outside," he said. A medical source in Hilla said three people were wounded in the explosions.