The Mail reports that Kathleen Danby, 72, was ordered to be jailed by the secretive Court of Protection, which had banned her from making contact with the 18-year-old.
She had earlier been told she could only speak to her grandchild on the phone once a month at a set time, with social workers listening in. The reasons for ruling haven't been disclosed.
But when social workers heard that she had met the girl at a model railway exhibition and had been filmed her hugging her granddaughter outside a pub, she was ordered back to court.
At a hearing in Birmingham, Judge Martin Cardinal ordered that Mrs Danby should be jailed for three months.
However, Mrs Danby, who lives in Orkney, wasn't in court and told the Mail that no police officers had arrived to execute the warrant.
Mrs Danby said the girl was moved into care in Derbyshire in 2007, when she was 11, a year after being removed from her father in Orkney.
She told the newspaper he was banned from seeing her after he was convicted for ill-treatment after restraining her from running into a busy road while she was having a temper tantrum.
She said the girl's father has since been jailed twice for trying to contact her – once for waving at her taxi as she travelled to school.
Judge Cardinal said the girl, named only as B, finds it hard to control her anger, has self-harmed and frequently runs away and social workers believe her distress increases when she is contacted by her father or grandmother.
Derbyshire County Council said Mrs Danby broke the injunction banning contact by meeting her granddaughter outside the pub next to a care home in February.
Four days earlier, the teenager escaped from her minder and took a circuitous route to the town of Chapel-en-le-Frith.
Judge Cardinal said the girl knew that for the last three years her grandmother has attended a model railway show there in February.
She told a care worker that her grandmother had come from Scotland to see her.
He said: "I am sure this grandmother needs restraint."
However, as yet, it has not been revealed why Mrs Danby is banned from seeing her granddaughter.