"If you decide, against the rules, to take part in Paris-Nice, you will be heavily penalised," McQuaid is quoted as saying by L'Equipe in a letter sent to four French teams -- AG2R, Francaise des Jeux, Cofidis and Bouygues Telecom.
The week-long race, which starts on March 11, was dropped from the UCI's Pro-Tour following a dispute with organisers Amaury Sport Organisation (ASO).
"I cannot imagine being punished. Why would people be prevented from doing their job?," Francaise des Jeux manager Marc Madiot told the paper.
"If we cannot race, we are consequently not allowed to do our job," his Cofidis counterpart Eric Boyer added.
Rabobank, T-Mobile, Gerolsteiner and France's Cofidis, Bouygues Telecom and Francaise des Jeux said last Friday they would defy the sport's governing body and compete in the race.
The UCI wrote to all 20 teams on its Pro-Tour, telling them it no longer recognised the race and ordering them not to enter.
The dispute dates back to January when the ASO, who also organise the Tour de France, turned down the application of Swedish team Unibet.com, a member of the Pro-Tour's elite.
Teams use the Paris-Nice as preparation for Pro-Tour classics such as the Milan-San Remo, the Tour of Flanders, Paris-Roubaix, the Fleche Wallonne and the Amstel Gold Race.
UCI officials asked for a meeting with ASO to try to settle the issue but no agreement has been found.
The UCI can refuse to send commissioners to the Paris-Nice but the federations of France, Italy, Spain and Belgium have said they are prepared to help the ASO with the race organisation.