The blast occurred in the southeastern Turkish province of Mardin and the cause was not immediately clear. The pipeline is hit intermittently by acts of sabotage, for which the terrorist Kurdistan Workers' Party (PKK) has in the past claimed responsibility.
The group calls the pipeline a strategic asset for the Turkish government and says its attacks are aimed at destroying it as a source of considerable revenue.
"Oil flow is continuing without problems through the pipeline," Yıldız said on Monday when speaking to a group of reporters in Kayseri province. Asked whether the blast was the result of sabotage, Yıldız said this had not been confirmed.
Turkey's Southeast, through which the pipeline runs, is the scene of a conflict between PKK militants and the Turkish state. More than 40,000 people have been killed in the fighting since the PKK took up arms in 1984.
The PKK said its militants had carried out an attack on the pipeline in the Midyat district of Mardin on Friday night, according to a statement on the website of the group's armed wing. It did not refer to any attack on Saturday night.
The oil in Kirkuk, in northern Iraq, is also at the center of a crisis within the Iraqi government of Sunni, Shi'ite and Kurdish parties over control of revenues, oilfields and territory. Kirkuk sits on the internal border between Iraq and the autonomous region of Kurdistan.
Kirkuk output has slumped to 280,000 barrels per day (bpd) from 900,000 bpd in 2001.