The House said Ibrahim Idris committed "several infractions" in the 2016 budget, adding that he refused to appear before a Police Committee.
The House alleged that Idris diverted the N1.8 billion which was voted in the 2016 budget for the purchase of 10 Armoured Personnel Carriers for the Nigeria Police.
The lawmakers said the money was, instead, used to purchase 64 Toyota Hiace "without the approval of the National Assembly."
A separate N6 billion was also voted for the rehabilitation of 102 police stations nationwide.
Therefore, the House has summoned the IG to come and defend the diversion of funds.
Gabriel Onyenwife, a member from Anambra State, moved the motion to summon the IG, saying he had ignored all invitations sent to him by the Committee on Police Affairs asking him to appear before the committee.
According to the resolution to summon Idris, he may be arrested through a warrant of the House if he fails to before the committee on January 19.
The resolution reads in part: "The House is concerned that the persistent failure or refusal of the IGP to honour the invitations has stalled the investigation into the diversion of the funds.
"The House condemns in strongest terms, the failure of the IGP to honour the invitation of the Committee on Police Affairs.
"The House resolves to cause a bench warrant to be executed for the arrest of the IGP for the purpose of his appearance before the committee in the event of his refusal or failure to appear on January 19, 2017."
The House said it only highlighted two out of the "several infractions" committed by Idris in the 2016 budget.