The girl, who signed her name as Faith, sent the letter after she accidentally broke the decoration while visiting a shop in Cambridge.
She stuck two £1 coins to the note, which she posted to the "Christmas Department" of the store.
The letter read: "To John Lewis Cambridge. I'm sorry I broke a Christmas bauble on Saturday. It cost two pounds. Here is the money for it. Sorry again, Faith, aged 5."
Staff now want to find Faith to thank her for the gesture, and searched for her using Twitter, saying: "Are you Faith the Cambs xmas bauble breaker? John Lewis want to say thank you!"
Branch manager Dominic Joyce said he hoped to find Faith, who addressed her letter to the John Lewis Christmas Department, so she could be given some treats.
He said: "We don't have much to go on - just a first name, a Cambridge postmark and what might be a self-portrait.
"It's a possibility that she and her parents want this to be a nice gesture and don't want any thanks. But if they do come forward, we would love to thank Faith.
"We get lots of nice letters but nothing quite as special as this."
He added that because the girl had visited on one of the store's busiest weekends, nobody had noticed the broken bauble.
Mr Joyce also tweeted: "The cutest letter sent to JL Cambridge. There is no address so we wanted to thank Faith on Twitter."