The husband had allegedly paid Rs 13,000 to the clinic for the pregnancy termination after an ultrasound imaging showed the foetus had deformity.
The AIIMS medical board told the high court that the termination procedure would be "reasonably safe" at the present stage of gestation of the pregnancy.
Justice Singh, before granting the permission, also spoke to the woman's husband to find out whether he understood the risks associated with the procedure.
The woman, who was accompanied by her mother, told police that the accused raped her at gunpoint five months ago and had threatened her with dire consequences if she revealed it.
The Supreme Court today allowed a woman to terminate her pregnancy, relying on a medical report that the 26-week-old foetus was without a skull and would not be able to survive.