After his second goal at Stamford Bridge, which put Arsenal 4-3 up, the Dutchman was seen touching his shoulder with his right hand before raising it to the air.
The claims, published on the internet, were brought to Van Persie's attention after the match but he was quick to label them "insulting and absolutely absurd".
"It has been brought to my attention of some ridiculous allegations concerning my celebration of one of my goals yesterday," Van Persie said on Twitter late Sunday.
"It is totally ludicrous to suggest that my action of brushing my shoulder and pointing to my fans could be construed as anything else but of a showing of joy and celebration."
"To suggest this meant anything to the contrary is insulting and absolutely absurd as nothing else came into my mind."
Van Persie plays down 'Nazi' salute claims
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