Fury about the film, produced in California, swept across the Middle East after Friday prayers, with protesters attacking US embassies. On Tuesday - September 11 - an attack on the US Consulate in the Libyan city of Benghazi killed the US ambassador and three other Americans in related violence.
"Whoever comes across America's ambassadors or emissaries should follow the example of Omar al-Mukhtar's descendants ( L ibyans), who killed the American ambassador," Yemen-based Al Qaeda in the Arabian Peninsula (AQAP) said.
"Let the step of kicking out the embassies be a step towards liberating Muslim countries from the American hegemony," it said in a statement posted on a website.
At least 17 people have been killed since Tuesday in the violence, which prompted Washington to send troops to bolster security at its missions.
AQAP, mostly militants from Yemen and Saudi Arabia, is regarded by the United States as the most dangerous branch of the network founded by Osama bin Laden.
"The film published in America which insults our Prophet Mohammad, peace be upon him, comes as part of the continuing crusader wars against Islam," AQAP's statement said, referring to European wars in the Middle East about 1,000 years ago.
"The incident is so huge that the resources of the nation should be pooled together to kick out the embassies of America from Muslim lands," it said.
AQAP has used Yemen, a regional US ally, as a base to plot attacks on the United States. Washington has backed a Yemeni army campaign that drove Al Qaeda and its allies from their southern stronghold this year.
Praising the attacks by demonstrators in Libya, Egypt, Yemen and Sudan on US and other Western missions, the AQAP statement said American embassies should be burned and envoys killed. It said defending the Prophet's honour was a "religious duty".
The group also said Muslims living in the West had an extra duty to be involved in attacks. "They are more capable of doing harm and reaching the enemy is easier for them," it said.
In a second statement, AQAP said Tuesday's assault on the US Consulate in Libya, and the killing of Ambassador Christopher Stevens, was partly motivated by the death of Abu Yahya al-Libi, a Libyan Al Qaeda leader in Pakistan.
Libi was killed in a drone attack in June but the militant group announced his death only on Tuesday
"The killing of Sheikh Abu Yahya only increased the enthusiasm of the proud, jihadi people of Libya and their determination for revenge against those who mock our religion and defame our prophet ... so they stormed the American consulate and killed the ambassador," said the statement, posted as a eulogy to Libi.
Protesters have blamed the US government for the amateurish film of obscure origin which triggered protests. Washington has condemned the film and said it does not condone any insult to any religion.
Impoverished Yemen is struggling against challenges on many fronts since mass protests forced president Ali Abdullah Saleh to step down last year after decades in power.
The United States, eager to help the country recover from the upheaval that has pushed it to the brink of collapse, has said it would provide $345 million in security, humanitarian and development aid this year, more than double last year's aid.