Kent Police said in a statement that the man, from Aylesham, was detained last night on suspicion of making malicious telecommunications and that he was in custody awaiting interview.
The force does not say whether the arrested man actually burned the poppy, or just posted the photo online.
The arrest was met with incredulity on Twitter, where people mounted a fierce discussion over civil liberties.
Tom Williams, tweeting as @tomwilliamsisme, wrote: ''The scary thing is, the man wasn't arrested for burning a poppy - that's not illegal. He was arrested for putting it online.''
Jamie's Pants, under @thisisrjg, tweeted: ''We do not have a right to not be offended. We certainly don't have a right to lock up someone for offending some people'', while Thom Lumley, tweeting as @Hotstepperrr, wrote: ''Dear idiots at Kent Police, burning a poppy may be obnoxious, but it is not a criminal offence.''
David Allen Green, a journalist and lawyer for the New Statesman, tweeting as Jack of Kent, wrote: ''What was the point of winning either World War if, in 2012, someone can be casually arrested by Kent Police for burning a poppy?''
Australian musician and comedian Tim Minchin also tweeted his incredulity, saying: ''You've a right to burn a (fake!) poppy. Whether I agree with the action is utterly irrelevant. Kent Police are out of line.''
No-one from Kent Police was available to comment.
Nick Pickles, director of civil liberties campaign group Big Brother Watch, criticised the arrest as "utterly ridiculous".
He said: "Kent Police need to urgently release this man and drop an utterly ridiculous investigation into something that has harmed no-one.
"It is not illegal to offend people and, however idiotic or insensitive the picture may have been, it is certainly not worthy of arrest.
"This case highlights the urgent need to reform a law that poses a serious risk to freedom of speech after several ludicrous prosecutions in recent months