There was no immediate claim for the bombing which targeted a patrol in the Tarmiya district, around 30 kilometres (20 miles) outside the capital.
The area is a known hotspot for Islamic State group sleeper cells, who remain active five years after Iraqi authorities proclaimed victory over the jihadists.
A lieutenant-colonel was killed in the blast along with two of his men, the ministry said.
Three soldiers were also wounded, a separate security force statement added.
Tarmiya's orchards and palm groves are criss-crossed by a network of irrigation channels that make the area an ideal hideout for militants.
Iraqi counter-terrorism units carry out regular search operations in the area in a bid to prevent it being used as a launchpad for attacks but the terrain favours the sleeper cells.
IS is a shadow of the force that swept through large swathes of Iraq and neighbouring Syria in 2014 and imposed its murderous sectarian rule.
But it can still call on an underground network of between 6,000 and 10,000 fighters to carry out attacks on both sides of the porous border, according to a UN report released earlier this year.
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