The convoy was en route to Arbil from Mosul in the north of the country when the bomb exploded.
"The Foreign Minister has spoken to the consul general who is in good health," the spokesman said. "We are still investigating as to who carried out the attack and whether the consul general had been the target."
Relations between Ankara and the central Baghdad government have been strained in recent years, mainly due to Turkey courting Iraqi Kurds in the autonomous north for their energy reserves, and also over their differing stances on Syria.
Baghdad says it alone has the authority to control export of the world's fourth largest oil reserves, while the Kurds say their right to do so is enshrined in Iraq's federal constitution, drawn up following the US-led invasion of 2003.