Organisers apologised for the problem, which has been blamed on a "human programming error".
Glasgow 2014 said it is working to refund the charges to affected customers "as soon as possible".
The latest glitch comes after the ticket sales website was hit by problems, with customers facing delays of more than 30 hours when extra tickets went on sale on Monday.
The website and phone line have been closed while the issues are investigated and could remain shut for days.
The Daily Mail reported that some customers ran up bills of more than £100 while trying to buy tickets through the hotline.
A Glasgow 2014 spokesman said: "Glasgow 2014 can confirm that some callers to the Glasgow 2014 ticket line who received an engaged tone on the ticketing phone lines were charged in error by TalkTalk Business, a supplier of Ticketmaster.
"We apologise unreservedly for this and are working now with Ticketmaster and TalkTalk Business to ensure customers affected by this are refunded these charges as soon as possible."
An extra 100,000 tickets across all 17 sports and the opening and closing ceremonies went on sale on Monday.
A TalkTalk Business spokesman said: "It has come to our attention that due to a human programming error, we did not deliver the service that had been agreed with Ticketmaster during the general ticket sale for the Commonwealth Games.
"This meant that some customers who called the Commonwealth Games ticket line and received the engaged tone were charged for the call costs in error.
"We would stress that this issue did not affect all callers to the ticket line and we sincerely apologise for the inconvenience this has caused. We will work with Ticketmaster to urgently compensate all customers affected by this error."
Around 55,000 tickets have so far been sold from the latest ticket release, organisers said.
About 2.3 million applications were made for the initial one million tickets released last year, with athletics, aquatics and cycling proving the most popular events.
BT said it had contacted some customers about their calls to the hotline.
A BT spokeswoman said: "We contact customers if we see unusual or excessive usage on their lines to alert them to the change in their calling pattern.
"In this case, although the caller didn't speak to anyone, the calls were connected to the receiving number and the relevant charges were correctly raised.
"In the last 24 hours, we've warned a very small number of customers about their calls to Ticketmaster. BT is not part of the Glasgow 2014 ticketing operation."