Many spent hours online trying to secure some of the 250,000 new tickets released at 11:00 BST on Thursday.
"Failed to get #CursedChild tickets after queuing for four hours," wrote one Twitter user. "Now loads on sale for hundreds of pounds on StubHub."
Tickets are currently being offered on the secondary site for up to £1,000.
Admission for the two-part stage production bought from official vendors Nimax and ATG cost significantly less, with tickets priced between £15 - £70 per part.
A spokesperson for the show said although the newly-released tickets had sold out, returned and other late release tickets would become available daily.
There is also an online lottery on a Friday in which 40 tickets are released for every performance the following week.
The spokesperson added the show reserved the right to refuse admission to customers with tickets purchased on re-sale websites.
"Tickets purchased through either of our official ticketing platforms must not be sold or advertised for sale on the internet, in newspapers or elsewhere. Any ticket advertised for sale in this way will be automatically void," they said.
StubHub said its sales were "driven by supply and demand" and that sellers "set the price for what they think the market will bear".
Harry Potter and the Cursed Child became one of the hottest tickets in the UK long before its opening at the Palace Theatre in London in June.
Thursday's ticket release followed the publication of the script of the play, written by Jack Thorne and approved by Potter author JK Rowling, which became the fastest-selling book in the UK this decade.