The Gunners captain scored a hat-trick during Saturday's 5-3 success at Stamford Bridge, but his celebration after netting his second goal has prompted wild claims on the internet.
The Netherlands international has been accused of making a 'Nazi salute', but Van Persie has dismissed the allegations as 'ridiculous'.
"It has been brought to my attention of some ridiculous allegations concerning my celebration of one of my goals," wrote Van Persie on his Twitter account.
"It is totally ludicrous to suggest that my action of brushing my shoulder could be construed as anything else but 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."