Depends on how much of the face it covers, the California Court of Appeal seems to suggest.
Islam and American Law
The Appellate Court of Illinois reverses a trial court decision that deferred to a Muslim divorce from India.
A Pennsylvania court decision said they can (though relying on cases generally allowing restrictions on Public Trial Clause and First Amendment trial access rights in the interest of preventing embarrassment to witnesses).
A Michigan appellate court correctly enforces a Muslim couple's "mahr" agreement, entered at the time of the couple's marriage and calling for the husband to pay certain funds to the wife -- it's a valid contract, enforceable under secular law, regardless of its religious motivation.
"The change in the child's relationship with the father based on the child's fear of his displeasure if she were not a 'true Muslim,' and her belief that he threatened to abscond with her to Morocco, also contributed to the change in circumstances warranting modification" of the custody arrangement.