A photomontage, on his official website, appears to show the ex-US president playing golf in the shadow of a warplane or large drone.
The website image is captioned "vengeance is definite".
Twitter has suspended a small account which first tweeted the image.
A spokeswoman told Reuters the account - @khamenei_site - was fake and violated Twitter's platform manipulation and spam policy.
However, the post was also retweeted by Ayatollah Khamenei's much larger Farsi Twitter account with more than 300,000 followers. It has since disappeared from that account.