Militants targeted the North Sinai governorate headquarters with rocket fire during Iftar on Sunday, injuring three policemen, the Interior Ministry said.
The ministry added that rocket was launched from a long distance away and measured 168 centimetres by 25 centimetres.
The missile penetrated the third floor of the governorate building.
It was defused and the three victims given first aid, the ministry said in a statement posted on its Facebook page.
Three suspects were arrested following the incident. One of the suspects was said to be Palestinian.
Security forces meanwhile exchanged fire with militants who were travelling in two vehicles, the ministry said, with some of them being injured or killed.
The Interior Ministry added that, at approximately 9pm on Sunday, a bomb exploded near Arish Third police station, causing damages but no casualties.
Security forces are combing the area to search for perpetrators of the attack.