There was no immediate claim of responsibility for the attack in Tuz Khurmatu, which borders a province plagued by sporadic jihadist attacks.
Iraq declared victory over the Islamic State group in late 2017, but its jihadists remain active in the country, particularly in rural areas.
Sunday's blast killed an army regiment commander, another officer and a security service member, said Zulfiqar al-Bayati, mayor of Tuz Khurmatu.
A security official confirmed the death toll to AFP, adding the victims had been in a vehicle when the explosion occurred.
Those killed were members of the Peshmerga forces of the autonomous northern region of Kurdistan, while the wounded were members from the Iraqi army.
The Iraqi defence ministry paid tribute to the three soldiers who "fell as martyrs... while carrying out their duty".
The Islamic State group overran large swathes of Iraq and neighbouring Syria in 2014, proclaiming its "caliphate" and launching a reign of terror.
It was defeated in Iraq in 2017 by Iraqi forces backed by a US-led military coalition, and in 2019 lost the last territory it held in Syria to US-backed Kurdish forces.
A report by United Nations experts published in July estimated there were around 1,500 to 3,000 jihadists remaining in Iraq and Syria.
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