Inspector Emmanuel Akubo and Inspector Rufai Adamu, identified as the victims, were abducted alongside ASP Francis Idoko on Saturday, November 27.
The minister said the abduction was ordered by one Chinonso Okafor, and the beheading of the officers carried out by an IPOB operative he referred to as 'Gentle'.
"Chinonso Okafor, the most influential commander of ESN in charge of Imo and Anambra States, as well as 'Gentle' and all those who perpetrated the abhorrent act will be made to face swift and sure justice," he said.
IPOB had for years agitated for the secession of the south east region from Nigeria, and was designated a terrorist organisation in 2017.
The group continued its agitation and, since the creation of ESN, has been blamed by authorities for the spike in insecurity in the south east since last year.
The wave of violence has especially targeted security agents, dozens of whom have been killed in coordinated attacks.
Mohammed said on Monday the group's violent streak invalidates recent calls for a political solution to its agitation for an independent nation.
IPOB leader, Nnamdi Kanu, pleaded not guilty to an amended seven-count charge bordering on terrorism during a court appearance in Abuja last month.
He was re-arrested earlier this year after spending four years abroad since fleeing bail in 2017.