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In the video, the young rapper from Mecca, who identifies herself as Asayel Slay, praises what she describes as bold women in Islam's holiest city.
Wearing a headscarf and sunglasses, she describes the women as "sugar candy" in the song titled "Mecca Girl".
But Mecca governor Khaled al-Faisal has ordered the arrest of those behind the video, saying in a statement on Twitter that the video "offends the customs and traditions" of local Saudis.
The move underscores the limits of a recent Western-style liberalisation drive in a society steeped in conservatism.
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The statement sparked indignation on social media, with many tweeting their support under the hashtag "Mecca girl represents me".
"I am from Mecca & the only thing I find offensive is your racism, misogyny and your war on a young woman & her artistic expression of her culture & her people," said one Twitter user.
"This is so typical for the #Saudi government -- bring Western influencers to artwash the regimes crimes but attack real Saudi women who try to artistically express their cultural identities," tweeted Amani al-Ahmadi, who calls herself a Saudi feminist.
"This is racist, sexist."
A host of Western women musicians –- from Janet Jackson to Mariah Carey and rapper Nicki Minaj -- have been invited to perform in the kingdom as its eases its tight restrictions on various forms of entertainment, in a bid to shake of the country's ultra-conservative image.
Nicki Minaj however pulled out of the concert in what she described as a show of support for women's and gay rights in the kingdom.
De facto ruler Crown Prince Mohammed bin Salman has scrapped decades-old bans on cinemas and women drivers while allowing gender-mixed concerts and sports tournaments.
The relaxed social norms have been welcomed by many Saudis, two-thirds of whom are under 30.
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