Ahmed, a moderate Islamist, was elected in January to lead the civil war-torn African nation following U.N.-led reconciliation talks, according to the Agence France-Presse.
He was a leader of the Union of Islamic Courts, which controlled Mogadishu in 2006 before being ousted by Ethiopian forces, the BBC reported.
In the 12-minute tape, which could not be immediately verified, bin Laden said, "This Sheik Sharif ... must be fought and toppled. ... He is like the (Arab) presidents who are in the pay of our enemies."
Islamist fighters, who have been fighting the Somali government since before Ahmed became president, are seeking the withdrawal of all foreign forces and the reinstatement of Sharia law. Islamist guerillas now control much of southern and central Somalia.
The Somali cabinet on Tuesday reportedly agreed to introduce Islamic law, which will be presented to Parliament for approval. But bin Laden warned the militants against waiting for Ahmed to implement Sharia law.
"My Muslim brothers in Somalia: you must beware of the initiatives which wear the dress of Islam ... like the initiative attributed to some of the Ulama (scholars) of Somalia which gives Sheik Sharif six months to implement Islamic Sharia.
"They are asking him (to build) something he was in fact installed to demolish," bin Laden said, according to the AFP. "It is a duty to fight the apostate government and not stop the battle."
Bin Laden also issued an audio recording on Saturday that labeled the Israeli offensive last winter against Hamas in the Gaza Strip as a "holocaust."
He released a similar recording in January when he urged a holy war to liberate the Palestinian territories.
Bin Laden has a $25 million U.S. bounty on his head.