Hackers said they had penetrated Hacking Team's internal network and stolen more than 400GB of data.
The Italian company said it was working with police to track down the hackers.
Widely shared online, the stolen data includes a list of the countries that have bought Hacking Team's main surveillance tool, Da Vinci, and emails suggesting intelligence agencies use it to spy on activists and journalists.
The list includes:
Lists of passwords and login details for client sites were also revealed.
The hackers first published stolen data, including internal files, email messages and software source code, on Hacking Team's own Twitter account, having first changed its name to "Hacked Team".
Confirmation of the breach came via the Twitter account of Hacking Team engineer Christian Pozzi.
"We are awake. The people responsible for this will be arrested. We are working with the police at the moment," he said in one message.
Soon after, this and other messages about the breach were removed as Mr Pozzi's Twitter account was deleted.
Hacking Team's website is also currently offline.
Security expert Graham Cluley said the company had "no shortage of online enemies around the world".
Its software had been popular with intelligence agencies in many countries, he said, but he questioned how many would continue that relationship given that it had been "so seriously breached".
Human rights group Reporters Without Borders had named Hacking Team as one of its "enemies of the internet" because its software was being used in countries that did not have a "good record on democracy and human rights".

Watson's deal expires at the end of the season, but he says he has a "sense of unfinished business" at the club.
"I want to stay," the 25-year old told BBC Scotland ahead of Edinburgh's derby against Glasgow Warriors on Monday.
"At this point in time, I'm doing well for Edinburgh, and the best place for me to keep getting capped is playing in Scotland."
Edinburgh have finished no higher than eighth in the past five Pro12 seasons, and Watson, who played every minute of Scotland's three autumn internationals, wants to follow back-row colleague Magnus Bradbury in pledging his future to the capital side.
"Even though this is my sixth season, it's quite frustrating, because we win really tough games, and once we put together a season, this squad can achieve big things, and I don't want to miss that," he said.
"Definitely, there is a sense of unfinished business. I believe in the next two years we can achieve a lot if we hold on to all of our players."

Andrew Whitby, 51, from Teddington, south-west London, was recognised by the Guinness Book of Records.
He underwent the operation after experiencing health problems associated with a lifelong heart defect.
He appealed for people to sign the organ donor register, describing transplantation as "life-changing".
Figures published by the NHS on Monday show the number of people in the UK donating organs after death has fallen for the first time in more than a decade.
Mr Whitby was born with a hole in the heart, which doctors predicted would mean he was unlikely to live more than a few years.
He defied expectations and lived normally until the age of 20, when his health began to deteriorate.
Mr Whitby developed problems with his lungs and eventually one collapsed, which led to the decision to attempt a heart-lung transplant.
When the procedure was carried out in 1985 at Harefield Hospital in north-west London, he was only the ninth person to undergo it in the UK.
Heart-lung transplants are relatively rare because there are few suitable donor organs available and priority is normally given to people who only need a heart transplant.
Mr Whitby used the occasion of the 30th anniversary of his transplant to draw attention to the need for organ donors.
He said: "My heart-lung transplant has improved and extended my life beyond measure.
"We need more people to sign the organ donor register - without donors, where would that leave people like me?"
Andre Simon, director of transplantation at Harefield Hospital, said: "Andrew's world record shows how a person's life can be completely transformed through the gift of organ donation."
A company that sells surveillance software has been hit by a data breach.
[NEXT_CONCEPT]
Scotland flanker Hamish Watson says he "wants to stay" at Edinburgh beyond the end of his contract.
[NEXT_CONCEPT]
A man has celebrated 30 years since his heart-lung transplant - thought to be the longest anyone has survived after the procedure.