Mrs Justice Parker ruled that the woman clearly lacked the mental capacity to consent to marriage and it should be a "nullity" in England.
The judge rejected the family's argument that the marriage was in the woman's best interests.
The woman, whose identity is not being made public, is unable to perform basic daily tasks and has learning difficulties which are described as very significant.
In 2003, the woman's parents arranged for her to marry a cousin in Bangladesh who was subsequently given permission to come and live with her in the UK.
Police intervened when the marriage came to the attention of the local authorities.
In the latest ruling, the judge said the marriage should be annulled.
The parents argued that they were trying to give their daughter security by finding her a husband, and that annulling the marriage would bring shame on their family.
More than 50 such cases were referred to the Foreign Office and Home Office's specialist Forced Marriage Unit last year.
Last week local councils in England introduced measures to try to tackle the problem.