The incident happened on Monday at the Baba Kompo Registration Centre in the Asawase Constituency of the Ashanti Region.
A viral video shows the policeman in a heated confrontation with the self-acclaimed National Security operative.
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The latter then pulled a gun on the police officer, as some military men at the centre tried to separate the feuding pair.
Reports suggest the police officer was at the Centre at the instance of the Member of Parliament, Alhaji Mohammed Mubarak Muntaka.
In a statement, the Police administration said it has identified all the uniformed officers involved in the incident and has launched an investigation.
“We are investigating a video on social media in which a person in apparent civil dress is seen brandishing an object, which appears to be a pistol in the face of a Police Officer, with Soldiers apparently calming tensions down,” the Ghana Police Service posted on Twitter.
“All the uniformed persons in the video are known officers who are presently stationed in the Ashanti region, where the incident took place. They all reported the incident to their commanders on Monday 27th July 2020 when it occurred," it added.