Last week, a man fell to his death after taking part in a cocktail evening, which was set up over online social network Facebook and drew almost 10,000 revelers. The death was the first on record as a result of so-called Facebook aperitifs.
Such parties take place across France and often turn into huge drinking binges, alarming the authorities which are struggling to curb the phenomenon.
Since the death, French authorities have refused to ban the events outright, but have requested they are flagged in advance and supervised.
"Without underestimating the friendly motivation driving potential participants ... the police once again advises against the use of the site of the Champ de Mars this Sunday, May 23 at 1800 (1600 GMT)," the statement from police headquarters said.
Paris police said last week consumption of alcohol in the area, which covers the grounds of the Eiffel Tower, had been banned since June 2008.
With temperatures soaring in the French capital on Sunday and people already out in droves, the police are making a last ditch attempt to warn people before the event starts.
The police said that all necessary measures would be taken to cope with attempts to hold the drinking event but added that they were ready to look into allowing "convivial cocktails" if they took place in a suitable area and at a reasonable time.
Officers were already involved in policing other events including the start of tennis' French Open championships and the transformation of the Champs-Elysees into a giant farm.
Fifty-eight giant cocktail parties have been held in France so far, authorities say, with 32 more planned, including the one in Paris on May 23.
