In a post on X, Israeli army spokesperson Avichay Adraee urged residents of four zones in Beit Lahiya on Gaza's northern edge to move to two designated areas
The blast caused damage to the building's doors and windows, police said.
No group claimed responsibility and there was no comment from Halbousi or the Iraqi government immediately for the incident.
A similar incident hours later targeted the Baghdad headquarters of the Azm party of another Sunni Muslim politician, Khamis al-Khanjar, police said, but caused only light damage.
There was no claim of responsibility for the second incident.
Iraq's parliament, newly elected after an October 10 general election in which the powerful Shia Muslim cleric Moqtada al-Sadr was the biggest winner, voted to reinstate Halbousi for his second term as speaker on Sunday.
Shia parties aligned with Iran and which rival Sadr, opposed the selection of Halbousi.