Waterstones opened at 8am for the book launch and had sold 25 copies by 10.30am.
A spokesman for the Sauchiehall Street store said: "We would have expected to sell a bit more by now. I think most people are waiting until they have read the reviews. It is such a departure for her.
"We are expecting to sell more copies at lunchtime."
However one eager fan headed straight to the book display near the front of the store and snapped it up in seconds.
Sogol Manbadi, 27, originally from Iran but now studying in Glasgow, said: "I think she's amazing. I'm really curious what it will be like."
James Aldridge, event co-ordinator, Scotland, at Water-stones, said: "We've had a phenomenal number of pre-orders for the book."
Rowling herself said of it: "I don't think everyone will like the book. But I'm proud of this book. I like it. It's what it's meant to be. As an author, you can't say more than that."