According to police officials, Naziran Bibi was passing by the shrine in the thickly populated Mozang area yesterday when the man threw acid at her and escaped.
The acid burnt Naziran's face and chest. Local residents took her to Sir Ganga Ram Hospital where the doctors described her condition as "very critical".
Police launched a search for the attacker.
Despite a new law that imposes strict punishment for acid attacks, such assaults against women have been reported from across the country.