Saudis on social networks have called for legal action against a writer and cleric who urged his Twitter followers to harass women cashiers.
He advocated harassment as a way of discouraging women from working.
Recently Saudi women have been allowed to work in public in shops, provoking a backlash from conservatives.
Hundreds of Saudis and other Arab tweeters attacked him, some asking him what right he had to stop women working, others accusing him of inciting sexual attacks.
Others have defended him, arguing that his tweet was aimed at preserving the country's deeply conservative Islamic identity.
One of Mr al-Dawood's arguments is that letting women work is tantamount to human trafficking - he claims they are being exploited to attract business.
But a number of Saudi women have tweeted to contradict him.
Traditionally Saudi women have worked as professors, teachers or doctors in all-female workplaces.
It is a sign of changing times in the country that women have not only been permitted to work with men, but that many have also seized the opportunity for jobs that once would have been seen as too menial.
But this has not gone down well with the powerful religious elite, which has shown its displeasure with similar moves, such as granting women the vote in the next municipal elections and letting them serve on the influential Shura Council.
But in defending the conservative position, Mr al-Dawood has gone out on a limb. It is not the least of the ironies of his position that it appears to transgress the deepest social and religious taboos in Saudi Arabia.
It is not, however, the first time he's courted such controversy - he has previously suggested that babies should be veiled to protect them from being sexually molested.
Another irony is that he has used Twitter to make his point, although in recent weeks the site has come under sustained attack from leading Saudi clerics for corrupting and misleading young Saudis.
To lighten the debate with a touch of humour, tweeters have been sharing a recent cartoon in a local newspaper. It shows a huge, authoritative Saudi man holding out his hand to deny entry to a veiled woman.
She, however, has already walked straight through him, leaving him looking surprised - and with a gaping hole in the middle of his body.