Influential cleric Muqtada al-Sadr called for the boycot during his Friday sermon in Kufa near Najaf.
"I suggest that a fatwa (religious edict) be issued by (Shia religious scholars in the Iraqi holy city of) Najaf, (the Iranian Shia religious centre of) Qom and al-Azhar (the Sunni Muslims' highest religious authority) ordering a boycott of French products," he said.
"If we cannot reach such a decision, we should at least threaten to do it."
Silence would encourage other countries, such as Germany, to follow in France's footsteps, al-Sadr warned.
A similar call was made by a Shia cleric in Baghdad on Friday.
"We condemn the French government's decision prohibiting the Islamic veil and we demand the liberty that France says it embodies," Sayyid Amr al-Husseini told 10,000 worshippers in the Shia-populated Sadr City district.
"We encourage a boycott of French products and call on Muslims in France to continue wearing the veil," he said.
And in the Sunni northern city of Mosul, hundreds of women marched on Friday evening to protest against the French move.
French Muslims are outraged by
the proposed new law
The protests followed months of heated debate in France after which a committee of French experts recommended banning "conspicuous" religious insignia" from state schools.
These include the Islamic hijab, the Jewish kippa or skullcap, and large crucifixes.
The commision argued that religious insignia are incompatible with the secular nature of France's public institutions.
French President Jacques Chirac has come out in favor of the ban, which he wants written into law by the start of the next academic year.
But French Muslims have reacted with outrage to the moves.
They say the hijab is compatible with France's secular tradition, and the decision is more likely to alienate France's five million Muslims rather than integrate them into society.