In a message to her 10 million followers on Twitter, the author reposted a West Midlands Police appeal for information to trace the 800-word work, which raised £25,000 for charity when it was auctioned in 2008.
The prequel's owner also lost irreplaceable items of jewellery with links to his late father when safes were stolen from his home in Kings Heath, Birmingham, between April 13 and 24.
Speaking to the Press Association, the Harry Potter fan, who does not wish to be identified, thanked Rowling for taking to Twitter to publicise the police appeal.
The document's owner said: "I was in Bangkok and I got an email from my sister to give her a call urgently.
"She said 'Your home has been broken into and your safes are gone' - then I knew my sentimental items had gone out the door.
"It (the prequel) was something I have been responsible for for nine years - it's a bit of a shock and it took a little while for it to settle in."
Responding to news of the theft, Rowling retweeted a picture of the manuscript with the message: "PLEASE DON'T BUY THIS IF YOU'RE OFFERED IT. Originally auctioned for @englishpen, the owner supported writers' freedoms by bidding for it."
The "extremely valuable" prequel, penned on both sides of the A5 postcard, was sold at Sotheby's to raise funds for English PEN, which promotes understanding through literature, and Dyslexia Action.
West Midlands Police issued a plea for information about the break-in in the hope that "the appeal goes far and wide among Harry Potter fans throughout the world."
Investigating officer Pc Paul Jauncey said: "The only people who will buy this unique piece are true Harry Potter fans.
"We are appealing to anyone who sees, or is offered this item for sale, to contact police."
Reportedly set three years before Harry Potter's birth, the prequel 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.
Anyone who knows the whereabouts of the postcard, or who has information about the break-in, is urged to contact West Midlands Police on 101 or Crimestoppers anonymously on 0800 555 111.