In the message, Zawahiri called on supporters to attack "the Crusader-Zionist coalition whenever possible" and urged Saudis to overthrow the kingdom's ruling family.
"Is it not about time that you get rid of this rotten regime... That will never defend you?" he said.
Saudi Arabia on January 2 executed 47 people, mostly jihadists convicted of involvement in Al-Qaeda attacks that killed Saudis and foreigners in the kingdom in 2003 and 2004.
Zawahiri said Nimr's killing was "one of the manifestations of the Saudi-Iranian competition for power in the region, but under the umbrella of protecting and complying with the interests of America.