Mr Justice Baker has decided that the Islamic marriage was "arranged entirely" by the man and the woman's father.
He said a ceremony had taken place at a time when the woman was vulnerable to influence and has ruled that the marriage is not valid under English law.
The judge, who examined evidence at a hearing in a specialist court, also concluded that the woman's father had spent her money "for his own purposes" with no intention of repaying her.
Mr Justice Baker had analysed the case at a hearing in the Court of Protection, where issues relating to people who lack the mental capacity to make decisions are considered, in London, and has outlined his conclusions in a written ruling.
The judge, who heard evidence from witnesses including medical specialists, a social worker, an Islamic law expert and the woman's father, said the woman could not be identified.
He said she had links to London and Northampton and said the marriage, solemnised by an imam, had taken place at the Northampton Islamic Centre.
Mr Justice Baker indicated that investigations had started after one of the woman's female relatives raised concerns about forced marriage.
"(The man's) primary motive for marrying (the woman) was to achieve an improved immigration status," said Mr Justice Baker in his ruling.
"(Her father) knew that this was his primary motive."
The judge said the woman's father's motives were "more difficult to discern" and added: "I conclude that he acted partly to assist (the man) in his immigration application but also because he thought it would be right for (the woman), and the family as a whole, for her to be married."
He said the marriage was "arranged entirely" by the man and the woman's father and that the woman was "unquestionably married under the influence of her father".