The incident, which was caught on film and swiftly did the rounds on social media, happened in the heat of the stage 14 struggle on Saturday as the Slovenian Pogacar was breaking away from the defending champion.
The bare-torsoed spectator appeared to toss the potato chips into the faces of both riders with witnesses saying he was removed by police within five minutes of the incident.
"I do not understand people who go to a bike race to throw potato chips," said two-time title-holder Vingegaard at the finish.
Professional riders union CPA say they intend to sue the spectator.
The fan was allegedly too drunk to make a statement so police held him overnight in order that he could do so Sunday morning.
Pogacar won the stage to keep the yellow jersey and extended his lead over second-placed Vingegaard to 1min 57sec.
