"The response will be what you see and not what you hear and let our mothers bereave us if we do not make victorious our messenger of God," he goes on to say without specifying what action will be taken.
The five minute message which featured English subtitles could not be independently verified but it bore the logo of al-Qaeda's media wing al-Sahab.
The message also coincided with the fifth anniversary of the US-led invasion of Iraq.
The cartoons were first published by the Danish daily Jyllands-Posten in September 2005 but a furore erupted only after other papers reprinted them in 2006.
At least 50 people were killed in the protests against the publication of the cartoons, which some Muslims say are an affront to Islam.
In the past month, thousands of Muslims in Sudan, Afghanistan and Pakistan have protested against Danish newspapers reprinting the cartoons.
Sudan also barred Danes from the country and declared a national boycott of Danish products.
Newspapers which have reprinted the cartoons argue they are defending the right to media freedom.
Wednesday's message is believed to be bin Laden's first for 2008 and follows up an hour-long, audio missive from December 27 in which he warned Iraq's Sunni Arabs against fighting al-Qaeda in Iraq and vowed new attacks on Israel.
In November, he urged European countries to end military participation with US forces in the Afghan conflict.
The Saudi-born al-Qaeda leader, blamed for the September 11, 2001 attacks on US cities, issued a number of messages late last year after a hiatus of well over a year raised speculation that he might be dead or incapacitated.
He is believed to be hiding in remote areas between Pakistan and Afghanistan.