Justice J B Pardiwala rejected the plea while stressing on laws which cannot permit medical termination of pregnancy after 20 weeks since it could endanger the woman's life.
The High Court directed the Botad district Superintendent of Police (SP) to take over investigation of the rape case.
The HC also ordered the Botad district collector to keep a close watch on the gangraped woman's family members, including her husband, in order to ensure that all medical facilities are given to the woman to deliver her child.
"I am conscious of the fact that to carry a child in her womb after an act of rape is not only extremely traumatic for her but also humiliating, frightening and psychologically devastating. In Indian society, she becomes an object of scorn and ostracisation. This is very unfortunate," Justice Pardiwala said in the 38-page order.
"However, at the same time, assuming for the moment that termination at this stage is permissible, there would be a likelihood of danger to the life of the applicant in case of carrying out termination of pregnancy. If labour is induced to carry out termination of pregnancy, in every possibility, the same would result in a live birth of a new born as maturity of foetus is 28 weeks," the order said.