The women - some of whom were said to be older with medical conditions - were attending the world premiere of Cate Blanchett's new film Carol.
Screen Daily said the festival had confirmed heels were obligatory for women at red carpet screenings.
However the director of the festival said the "rumours" were "unfounded".
'Buy appropriate shoes'
Thierry Fremaux tweeted: "For the stairs, the regulations have not changed: 'No smoking, formal wear'. There is no mention of heels."
A note about dress codes on the festival's website appears to reinforce his point. It says "black tie /evening dress is required for gala screenings" - with no guidance on heel height.
Screen Daily first reported the story, after a "Cannes regular" told them how a woman wearing Rhinestone-encrusted flat shoes was denied entry.
The unnamed source said: "Someone I know was turned away for wearing nice flats, nothing you would wear to the beach. They were in their 50s. They told her she could go and buy appropriate shoes and come back."
Asif Kapadia, whose Amy Winehouse documentary screened at the festival last weekend, also tweeted that his wife had been challenged over wearing flat shoes, although she was eventually allowed in.
(BBC)
