The directorate said the rockets were fired from al-Hamdaniya district in Nineveh governorate.
They landed near Zey Gawra field oil refinery, causing no casualties or material damage.
According to Esta Media Network two of the rockets landed inside the refinery and two others fell outside.
The refinery is located in Kawrgosk in Khabat district in Erbil province.
The refinery is owned by Kar Group CEO Baz Karim Barzanji and whose home was hit by Iranian ballistic missiles last month.
Reporter's code: 50101