In the eight-minute video, entitled "Onwards, Lions of Syria" and posted on an Islamist website, the Egyptian-born Zawahri also urged Muslims in Turkey, Iraq, Lebanon and Jordan to come to the aid of Syrian rebels confronting Assad's forces.
"Wounded Syria still bleeds day after day, while the butcher, son of the butcher Bashar bin Hafiz (Hafez al-Assad), is not deterred to stop," Zawahri, wearing his white turban and seated against a green curtain, said.
"But the resistance of our people in Syria despite all the pain, sacrifice and bloodshed escalates and grows," he added.
Zawahri took command of al Qaeda after Osama bin Laden was killed by US special forces in a raid in Pakistan last May.
A Muslim should help "his brothers in Syria with all that he can, with his life, money, opinion, as well as information", Zawahri says.
Syrian forces bombarded districts of the city of Homs on Saturday in a campaign to crush the revolt against Assad, whose ally Russia said it would not support an Arab League peace plan circulating at the United Nations.
Activists said seven people were killed in the latest attacks in a week-long government siege of Homs, which has been at the heart of the uprising which broke out 11 months ago.
"Our people in Syria, don't rely on the West or the United States or Arab governments and Turkey," Zawahri said in what is believed to be his second such message to Syrian protesters.
"You know better what they are planning against you. Our people in Syria, don't depend on the Arab League and its corrupt governments supporting it."
Arab foreign ministers will discuss a proposal next week to send a joint UN-Arab mission to Syria, after a uniquely Arab team failed to end Assad's crackdown on protests.
"If we want freedom, we must be liberated from this regime. If we want justice, we must retaliate against this regime," Zawahri said.
"Continue your revolt and anger, don't accept anything else apart from independent, respectful governments."
In July, Zawahri urged Syrian protesters to direct their movement also against Washington and Israel, denouncing the United States as insincere in showing solidarity with them.
Earlier this month, another video with Zawahri appeared on Islamist forums, announcing Somali militant group al Shabaab was joining its ranks in an apparent bid to boost morale and sharpen a threat to Western targets.