"One of the heroes of 'Qaedat al-Jihad' carried out a suicide operation on the morning of Monday," said the statement, signed by Mustafa Abu al-Yazid, one of Al-Qaeda's leaders.
The attack was "in revenge against the state of infidelity, called 'Denmark', that posted cartoons hostile to the messenger of Allah," the statement read, according to an English translation provided by Site, a US-based group which monitors Islamic militant internet websites and chat rooms.
"This operation is a warning to the infidel state and those who ride with it, so that they are deterred from their sin ... and so that they apologise for what they did," Yazid added.
Site said the message was posted across several forums.
Danish intelligence officials said earlier on Wednesday that the attack had been meticulously planned for a "long time and with precision".
Denmark's secret services have sent three experts to Islamabad as part of their investigation.
Victims of attack
One Danish citizen of Pakistani origin and two Pakistani employees were among the dead in the blast that badly damaged the embassy and the offices of a UN-backed aid agency.
Al-Qaeda called for attacks on Danish targets after Danish newspapers ran caricatures of the prophet Mohammed.
Danish newspapers first published the controversial cartoons in 2005, sparking violent protests in Pakistan and other Muslim countries.
Several dailies reprinted the sketches in February this year.
Yazid said al-Qaeda congratulated "the Pakistani mujahideen ... the pioneers of the religious fervor and Islamic zeal, who participated" in the attack.