The Spain international's brother Marc was issued with a fine when he stopped his car in a bus zone for 15 minutes while with Pique in the Port Olimpic area.
It is believed that Pique was furious with the officers after they claimed that his brother's car was obstructing taxis and other vehicles.
According to La Vanguardia, Pique got out of the car and said to the police officer: "You envy me because I'm famous. You are fining me because you're on commission, because you have no money and you need to make commission.
"I'm going to speak with your bosses and get you reprimanded. You think you are masters of the world because you wear that uniform and fine people.
"Your father's going to pay this fine - I'm not. You are a disgrace. Your profession makes me sick and the Guardia Urbana is a fucking disgrace."
Following the incident, Pique wrote on Twitter: "What I said has been exaggerated a lot, but in any case, I am sorry, I made a mistake and it will not happen again."
After the confrontation, the two brothers are believed to have entered Casino Barcelona.