A report by the ombudsman found that a series of failures resulted in the girl becoming "lost in the system".
It said that Islington Council failed to separate the teenager's need for help from her mother's homelessness application, and wrongly told her it owed her no duty.
The council has since tried to contact the teenager to offer her assistance but has been unable to do so. Her whereabouts are currently unknown.
The report reveals that the girl's mother approached Islington Council for assistance after being evicted from her housing association property in August 2017, and was placed in interim accommodation in another council's area.
She also contacted the council's children's services department at the time of her eviction to say she had nowhere to live and her daughter was about to become homeless.
The council's housing department found that the mother intentionally made herself homeless and so it did not have a duty to continue providing her with interim accommodation, while referring the girl, who was 16 at the time, to children's services in the council area she was staying.
The ombudsman's investigation found the council at fault for failing to provide services to the teenager when she was at risk of homelessness as it should have carried out an assessment to find out what duty it owed her.
Michael King, Local Government and Social Care Ombudsman, said: "Islington Council's failures in this case have led to a situation where there is genuine concern for the welfare of this young person, as the council can no longer get in contact with her.
"Councils need to recognise the separate duty they have towards children when their parents are made homeless."
In addition to trying to contact the girl in order to carry out an assessment of her needs, the council has paid her £400 via a relative for the distress caused as a result of its failure to support her.
The council has also told the ombudsman it has held a complaint learning meeting and disseminated the learning across the department.
"I welcome the steps Islington Council has already taken to share the lessons that can be learned from this investigation with its staff to help ensure this situation cannot arise in future," King said.
Islington Council has been contacted for comment.