They report that Pilny was breathalysed by police after the game and produced a positive result.
After only a few minutes of the game, stadium personnel, both teams, as well as his referee colleagues had noticed that something was off.
The referee then fell over and staff decided he was not in the right condition to officiate the match.
The apparently drunk referee had even lost his radio set in the tumble and was filmed being taken away from the field only seven minutes into the match.
Pilny was replaced by another member of staff, who saw the match to full-time.
Zdenek Broz, spokesman for the home team FK Pribram, said in a statement that the referee's condition had posed a threat to others at the game and that he was taken away by other members of staff who were officiating the match.
Broz said: 'It was an inconceivable performance by the fourth official. He was taken away by official staff.'
Marek Pilny has not commented on his performance and although as of yet no official report has confirmed that he was drunk, fans say it was obvious.
Martin Viznar, who had been watching the game, wrote on social media: 'I cannot believe that a trained sports official would act like this after only a few shots or some beers.'
Netizen Tonda Louka added: "It seems that referee should be blowing into a breathalyser rather than a whistle."
Miroslav Tulinger, the head of the league's refereeing commission, said: "Of course we know about the incident in Pribram and we will see to it being resolved. We will then inform everyone about the steps being taken."
The fourth official assists the main on-pitch referee and is a key member of the officiating team. He is supposed to watch the game and advise the referee, keeping a record of everything and making sure the team of officials make all the correct decisions.
The game was won 3-1 by the away team, SK Slavia Prague.
