The manuscript was penned on both sides of an A5 card for a charity auction nine years ago and sold for Â£25,000.
The untitled 800-word work was taken from Howard Road, Kings Heath.
Reportedly set three years before Harry Potter's birth, it features the schoolboy wizard's father James Potter, and godfather Sirius Black, when they were teenagers.
They are confronted by two "muggle" policemen after a high-speed motorbike chase but manage to escape on broomsticks.
The manuscript and jewellery were taken during the break-in between 13 and 24 April, West Midlands Police said.
The force is issuing the plea for information almost one month on, in the hope "the appeal goes far and wide among Harry Potter fans throughout the world".
Responding to news of the theft, Rowling retweeted a message issued by the police.
The writer said: "PLEASE DON'T BUY THIS IF YOU'RE OFFERED IT. Originally auctioned for @englishpen, the owner supported writers' freedoms by bidding for it."
Petty Peculiarity responded, saying: "Only thing to do is hand write thousands of them and flood the market!"
The prequel was among several works donated by authors, including Sebastian Faulks and Doris Lessing, to an auction held in 2008 to raise funds for English PEN, which promotes understanding through literature, and Dyslexia Action.
The burglary victim, who only wished his first name - Hira - to be published, said it took a while for the "shock" to set in after he learnt it was taken.
He said the work was "priceless" and if it was sold again legitimately it had the potential to raise more money for good causes.
"I don't think whoever took it or stole it or who might purchase it will really understand the benefits to people out there, what it can do," he said.
"If I can get it back, I'm over the moon, because I'm only going to be doing good stuff with it.
"If it's destroyed, or if it's lost, it's a great loss."
The burglary victim admitted he had only read one of the Harry Potter books.
Investigating officer PC Paul Jauncey said: "We are appealing to anyone who sees, or is offered this item for sale, to contact police."
A Harry Potter prequel handwritten on a postcard by JK Rowling has been stolen in a burglary in Birmingham.