"There was an attack with rockets and small arms on the prime minister's house," the official said on condition of anonymity.
Miitig and his family were in the house at the time of the 3:00 am (0100 GMT) attack, but escaped unharmed.
The premier's guards opened fire on the attackers, wounding two of them and arresting them, the official added.
The interim parliament passed a vote of confidence on Sunday in Miitig and his new cabinet, amid rising lawlessness in the North African nation dogged by power struggles between rival former-rebel militias.
Successive governments have struggled to control the myriad of ex-rebel militias that have carved out fiefdoms across the country.