Sheikh Abdullah Daoud, who is not affiliated with the government of Saudi Arabia, made his controversial edict during an interview on the Islamic al-Majd TV that aired six months ago.
His statement recently went viral on social networking sites, the New York Daily News reports.
According to Daoud, dressing infants and children in the traditional Muslim veils would reduce the sexual molestation of minors, though the cleric did not cite any evidence for his view.
On Twitter, where the story gained media traction, the response to the idea of covering up baby girls has been almost universally negative, the report said.
According to the report, Sheikh Mohammad al-Jzlana, a former judge at the Saudi Board of Grievances, told al-Majd TV that the fatwa was "denigrating to Islam and Shariah and made Islam look bad."