TV2 News and the Politiken news site say Lars Hedegaard was not injured in the shooting.
Both say the gunman came up to Hedegaard's Copenhagen home Tuesday on the pretext of delivering a package, and then fired at least one shot but missed the writer.
Copenhagen police confirmed that there had been a shooting without injuries. They wouldn't say whether Hedegaard was the intended target.
Hedegaard heads the International Free Press Society, a group that claims press freedom is under threat from Islam.
He was fined 5,000 kroner ($1,000) in 2011 for making a series of insulting and degrading statements about Muslims.
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