Twitter's information security director Bob Lord said about 250,000 users' passwords had been stolen, as well as usernames, emails and other data.
Affected users have had passwords invalidated and have been sent emails informing them.
Mr Lord said the attack "was not the work of amateurs".
He said it appeared similar to recent attacks on the New York Times and the Wall Street Journal.
The US newspapers reported that their computer systems had been breached by China-based hackers.
Twitter has 200 million active users.
Mr Lord said in a blog post Twitter had discovered unauthorised attempts to access data held by the website, including one attack that was identified and stopped moments after it was detected.
"This attack was not the work of amateurs, and we do not believe it was an isolated incident," he wrote.
Mr Lord did not say who had carried out the attack, but added: "The attackers were extremely sophisticated, and we believe other companies and organisations have also been recently similarly attacked."
"For that reason we felt that it was important to publicise this attack while we still gather information, and we are helping government and federal law enforcement in their effort to find and prosecute these attackers to make the internet safer for all users."
Internet security specialist Graham Cluley warned Twitter's announcement that emails would be sent to users may prompt a spate of spam emails "phishing" for sensitive information.
He says people should be cautious about opening emails which appear to be from Twitter.
"You have to be careful if you get hold of one of these emails because, of course, it could equally be a phishing attack - it could be someone pretending to be Twitter.
"So, log into the Twitter site as normal and try and log in to your account and, if there's a problem, that's when you actually have to try and reset your password."
Another expert in online security, Professor Alan Woodward from the University of Surrey, warned users to be wary of messages sent them by the hackers via Twitter itself.
"They can then send what's called direct messages," he said. "They can put malicious links in those."
"It really looks like it's coming from someone you know and you might respond to it, you'd go to the site and all of a sudden you find that actually you've got some malware on your machine which is then stealing your bank details or whatever."
On Thursday the New York Times linked the attack to a story it published alleging relatives of former Premier Wen Jiabao controlled assets worth billions of dollars.
China's foreign ministry dismissed the New York Times' accusations as "groundless" and "totally irresponsible".