The spectator had jumped over the safety railing that runs the length of the clubhouse side of the ground.
A second spectator also came onto the pitch, to try and diffuse the situation, which was quickly over.
Referee James Byng asked for both spectators to be ejected from the ground, and stewards escorted them out.
Fareham say the matter will be dealt with internally and Moneyfields are hoping they escape any FA fines.
Moneyfields chairman Pete Seiden said: ‘It all happened so quickly.
‘There was some handbags between two players, a spectator evaded a steward and jumped onto the pitch.
‘It was dealt with very quickly. The spectators were asked to leave the ground, and they left the ground.’
Seiden said the club had its usual 20 unpaid volunteer stewards at Dover Road for the game.
‘They all do different roles and then during the game are positioned around the ground.’
Asked if he thought Moneyfields would be fined as a result of spectators encroaching onto the pitch during a game, he replied: ‘I would hope not.
‘We did all we could to get everything sorted quickly.’
Moneyfields secretary Joe Albertella added: ‘It’s the first time I’ve known anything like this happen.
‘We had the same amount of stewards for games where we’ve had crowds 500, 300, 200, and not had anything like that.
‘Fareham have said they will deal with the matter internally.’
Fareham Town secretary James Craskell was unavailable for comment, while first team manager Pete Stiles declined to comment.