Those who attended the May 22 show at Manchester Arena were automatically eligible to register for free tickets, while the general public had the opportunity to purchase tickets on Thursday morning.
A Ticketmaster spokeswoman said: 'Sadly, over 10,000 unscrupulous applications have been made'.
People could buy up to six tickets via Ticketmaster for the charity concert, but the ticket-selling website refuses to let them be resold on its reseller sites GetMeIn and SeatWave.
Ticketmaster said demand was "always going to be extremely high", with more than 450,000 searches for the event on its site in 24 hours.
"We're working hard to get tickets direct to fans".
Those who were at the original concert have been offered free tickets, while the the remainder went on sale for 52 Dollars.
"We would like to reassure any fans that were at the show that they will receive a free ticket for One Love Manchester, provided we can verify their initial booking". We will continue to honour the ones we lost, their loved ones, my fans and all affected by this tragedy.
However, the company says over 25,000 people applied for the special passes, with many tickets quickly being put up for sale by scalpers on websites like eBay and Viagogo.