Christopher Gossage received the penalty after he told his wife's best friend, Judith Callegari, that the Edinburgh-based Harry Potter author was behind The Cuckoo's Calling.
Ms Callegari then revealed the secret via Twitter to a journalist.
Gossage, a partner in London-based Russells Solicitors, was found to have breached confidentiality rules and has been issued with a written rebuke by the Solicitors Regulation Authority.
In July, Rowling accepted a substantial donation to a forces charity from the London law firm.
The writer, who is worth around £500 million, brought proceedings in London's High Court against the pair.
The court heard Rowling, who had not wanted her authorship to be made public, had been left "dismayed and distressed" by the "betrayal of trust".
A sequel to the book is being lined up.
JK Rowling would not comment last night.