"The proper solution to this growing campaign of blasphemy is the execution of those involved," said the article.
The article singles out Seattle-based cartoonist Molly Norris, who satirically proposed to make a blasphemous page on Facebook, but it also said that the killings should not be limited to participants on the social networking website.
"Because participants are practizing a 'right' that is defended by the law, they have the backing of the entire Western political system. This would make, attacking any Western target legal from an Islamic viewpoint," the article said.
"We will fight against blasphemers. We will instigate, we will bomb, and we will assassinate, and may our mothers be bereaved of us if we do not rise in defense," it added.
US monitoring service SITE said that the Al-Fajr Media Centre, an Internet distribution network for extremist groups had released the magazine.
Awlaki purportedly inspired Islamic terrorists and is wanted by the CIA after becoming "operational" as a senior talent recruiter, motivator and participates in planning and training "for Al-Qaeda and all of its franchises".
With a blog, a Facebook page, and many YouTube videos, he has been described as the "bin Laden of the internet".