The family, who want to join their British husband and father in the UK, were required to submit biometric details on their visa application form but did not have anywhere in Afghanistan where they could obtain tests.
The ruling could help about 100 families in a similar situation who are thought to be in hiding in Afghanistan.
After the family brought the case, the home secretary conceded that they could apply to come to the UK without submitting biometrics, with the case considered on its merits.
Before the case was brought, the home secretary said the biometrics requirement would not be waived. The judge, Mr Justice Knowles, said in his judgment the change by the home secretary was a “crucially important development”.
Nina Kamp, of Duncan Lewis solicitors, representing the family, welcomed the decision about the biometrics.
“This is a major victory as it will provide a potential way out of Afghanistan for this family and others in their situation.
“For now, the ability of the mother and her five children to leave their dire circumstances in Afghanistan is a priority. We are delighted for our clients that this is now a real possibility.”
A Home Office spokesperson said: “The taking of biometrics information, in the form of a facial image and fingerprints, is vital to protecting national security and our border.
“In most circumstances, overseas applicants are required to enroll their biometrics before coming to the UK. However those facing exceptional circumstances can request for the requirement to enroll their biometrics to be waived or deferred.”