Nottinghamshire Police are conducting the inquiry after a supporter sent them film he shot as hundreds of excited fans raced onto the pitch after the promotion-clinching victory at Notts County.
A section of the video, the full version of which the supporter uploaded to YouTube under the name Pompey Blue, shows an officer making what could be seen as punch-like motions as he tries to restrain people.
It follows the sacking of a steward who was filmed kicking out in a bid to trip up supporters running past him at full pelt.
More than 4,000 Pompey fans packed the main stand at Meadow Lane on Easter Monday to watch their team win 3-1 to guarantee promotion from League Two.
The supporter who shot the video sent an email to Nottinghamshire Police saying he had rechecked his film after reading in The News about the steward who kicked out.
He told police: ‘I reviewed footage I shot at the recent Notts C v Portsmouth game and thought you may be interested in the conduct of one of your officers at this game.
‘The “interesting” footage appears between 1:04 - 1.20 into the following footage which shows two questionable conduct incidents involving the same officer.
‘The first incident I believe falls short of the standards expected of a member of your force whilst the second is very questionable.’
Nottinghamshire Police confirmed that an investigation had been launched.
A spokesman said: ‘Nottinghamshire Police’s Professional Standards Directorate has received a public complaint about the matter, which will be investigated in line with statutory guidelines.’