The Yemeni government has asked Washington to provide proof of its accusations against Shaikh al-Zindani in order to take judicial measures.
Shaikh al-Zindani, who is the dean of the Iman University and is a senior leader of the Islamist Islah (Reform) party in Yemen, said the demand for his arrest impinges on Yemen's sovereignty.
Yemen's Saba news agency said: "The United States has officially demanded from the Yemeni government to arrest Shaikh al-Zindani, freeze his assets and prevent him from travelling abroad."
Washington has been angered by the escape of 23 al-Qaida suspects from a jail in the Yemeni capital, Sanaa, prompting some US politicians to say the Yemeni authorities may have facilitated the jail break.
Yemen offered a reward of more than $25,000 for information that could lead to the capture of any of the men, including Jamal Badawi who was serving a 10-year sentence.