Chief executive David Grevemberg made the "unreserved apology" for the "disappointing situation" as the website was suspended at 6pm yesterday until the problems were fixed.
It followed a second day of lengthy waits for would-be buyers, who had already complained of glitches on Monday when the 100,000 extra tickets for the Games were released on a first-come, first-served basis.
The website was initially shut between midnight and 1am yesterday in an attempt to fix the problems, but as more and more people logged on in the morning, the glitches returned.
The difficulties meant just over half the extra 100,000 tickets have been sold, although a number of events including diving and triathlon have sold out.
Customers complained they were repeatedly being shunted back into the queue just as they reached the payment stage, while others found events sold out after a 24-hour wait online.
Some took to Twitter in despair after accidentally hitting the refresh button and losing their place in the queue, while others joked about a second day staring at the "circle of doom" on their computer screens.
Some customers said they had finally secured Glasgow 2014 tickets after 25 hours, having first tried on Monday.
In an attempt to finally iron out the technical difficulties, Games organisers ordered Ticketmaster to shut the ticketing website and call centre from 6pm yesterday.
Mr Grevemberg said: "At 5pm we instructed our official ticketing agent, Ticketmaster, to close the Glasgow 2014 ticketing website and call centre until we can be assured the technical issues being experienced by our ticket buyers over the last day and half are resolved to our satisfaction.
"From 6pm, no further customers will be able to join the website queue or access the call centre until further notice."
Customers logged on to the website before 6pm were expected to be able to complete the booking process, said Mr Grevemberg.
He added: "We want the purchase of tickets through the Ticketmaster system to be a positive experience for all customers and we realise this has not been the case for many.
"We thank everyone for their patience and apologise unreservedly to everyone who has been affected and inconvenienced by this disappointing situation."
By yesterday afternoon, organisers said a number of events, including swimming, diving, track cycling, mountain biking and the triathlon, had sold out, leaving some customers disappointed.
On Twitter, David Trice wrote: "Nooooooo ... After 24hrs of sitting in queues the diving is all sold out."
Another customer, Jayne Stirling, said: "Twice I've had tickets in my basket and twice I've been put back in the queue. So angry I have missed out."
Ticketmaster was appointed last May despite criticism over a "shambolic" sales process for the London 2012 Olympics, which saw the booking website struggle to cope with demand - either crashing or almost grinding to a halt.
There were more problems in the second round of sales when thousands of people thought that they had bought tickets, only to be told the following day that they would not be charged, as they had not got any tickets.
However, Ticketmaster said the system being used for the Commonwealth Games is very different to the one used for London 2012.