In a fatwa published on Monday, Shaikh Ibrahim bin Nasir al-Kudhairi said the channel was haram (forbidden) and a source of corruption.
A judge at the grand Islamic court in Riyadh, al-Kudhairi printed his religious ruling in al-Hayat newspaper.
He claims Alhurra is intended to "fight Islam … and support American hegemony", branding the staff who worked at it as "agents in the pay of America".
While admitting he had never watched the channel extensively, the religious scholar said he had read enough about it to justify his ruling.
"It seeks an Arab audience in order to weaken and control them" and wages "an intellectual war is currently being waged to rub out the Arab identity and Muslim religion".
The Broadcasting Board of Governors' Middle East Committee supervises Alhurra which is financed by the US Congress.
The channel was launched to improve the image of the United States in the Middle East.
It also intends to rival popular Arabic-language stations such as Qatar's al-Jazeera and Dubai-based al-Arabiya.