Sheikh Abdullah Daoud made the remarks during an interview with Islamic Al-Majd TV last October, but video of the interview recently went viral on social media sites and his 'fatwa' has been derided as absurd and a mockery of Islam.
Daoud claimed that baby girls would be protected from abuse if they wore a full burka, and justified his statement by citing unfounded medical reports of the sexual molestation of babies in Saudi Arabia.
According to Islamic law, girls are not required to wear burkas until they reach puberty.
Many Twitter users have condemned his remarks.
"Burkas for babies is disturbing! Now the baby victims are blamed for men's crimes. Allah help us stop the ignorance," one user wrote.
"Why stop with baby girls. Let's cover everything in a burka to protect the world from sexual abuse by men," another joked.
Sheikh Mohammad Al-Jzlana, a former judge for the Saudi Board of Grievances, condemned Daoud's statement as a mockery of Islam, and harmful to the religion's image.
He also appealed to Saudis not to pay attention to unofficial fatwas (religious edicts), and emphasized that such rulings can only be issued by Saudi authorities. He said that he feels sad whenever he sees a family walking around with a veiled baby, describing that as injustice to children.