Play.com said the incident took place in the early hours
Customers of Play.com have contacted the BBC to report problems with the online retailer's ordering system.
Many customers have received e-mails from Play.com reporting the despatch of an order they did not place.
Those opening the orders found contact details, including names and addresses, for other Play.com customers.
The problem appears to be widespread with many reporting Play.com help lines were jammed as they called to find out what had happened.
Simon Hurley from Clevedon near Bristol said he woke up this morning to find more than 80 e-mails from Play.com.
"I'm a big customer of theirs but not that big," he said. "I opened up each individual e-mail and it came up with another customer's name and their order."
Although there were no credit card details visible in the e-mails, Mr Hurley said all the messages had scrambled text at the bottom that could hide some information.
"People are being told to shred documents and then you have a big company like Play.com sending out hundreds of wrong e-mails to their customers," he said.
Mr Hurley said he rang Play.com to find out more but it took a long time to get through because the lines were "jammed solid".
Once he reached someone in customer services he was told that Play.com had a "massive problem."
So far it is not clear how many Play.com customers have received other people's e-mails nor how many e-mails have been sent out.
However, in other discussion forums on the web some customers talked about how many erroneous e-mails they had received.
On some forums customers said they were told that a "system error" was behind the sending of the e-mails.
In a statement a Play.com spokesperson said: "We were alerted to an incident that appears to have affected some customers for a short period of time in the early hours of this morning, and the first thing we'd like to say is that we apologise for any inconvenience our customers have experienced as a result.
"We'd like to reassure our customers that the cause of the incident has been identified and resolved.
"We take these matters very seriously and are now investigating how this incident occurred in the first place, so that we can prevent it happening in the future."
Play.com is among the most popular online shops in the UK for DVDs. CDS, games and movies. In February 2009, Play.com was the top retailer in the National Consumer Satisfaction Index.