Fourteen other officers were wounded in the attack, police General Mariano Botero said.
Botero, head of the Barranquilla police, said that one suspect was captured.
The bomb was detonated as the officers gathered for morning formation.
The blast initially wounded 17 police officers, but three died "due to the gravity of the wounds," Botero added.
Barranquilla Mayor Alejandro Char blamed drug traffickers for the attack.
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"I do not have the slightest doubt that this is a retaliation" for successful police action against drug traffickers, he told reporters.
"We will not rest until we find those responsible, my solidarity with the families of the victims and the wounded," Santos wrote.