"Anonymous" claimed they stole more than 4,000 credit card numbers, passwords and home addresses. The hacker group claims it stole Stratfor's confidential client list, which includes entities ranging from Apple to the U.S. Air Force.
"Not so private and secret anymore?" Anonymous taunted in a message on Twitter.
One hacker said the goal was to steal money from the accounts to give away as Christmas donations.
Some clients have reported unauthorized transactions.
"They're actually just costing us all time and money, and ruining my Christmas, or my holiday," said hacking victim Allen Barr. "Not my Christmas, just not my Christmas spirit."
Stratfor provides political, economic and military analysis to help clients reduce risk.
The hackers said they have enough targets to continue the attacks through the week.
The Associated Press contributed to this story.