It ended up in court after a falling-out between the woman and her daughter.
The judge ruled the matter was within the scope of the EU's General Data Protection Regulation (GDPR).
One expert said the ruling reflected the "position that the European Court has taken over many years".
The case went to court after the woman refused to delete photographs of her grandchildren which she had posted on social media.
The mother of the children had asked several times for the pictures to be deleted.