"Other banks are hit by this too," bank spokeswoman Kerstin Ottosson said.
Eurocard announced on Tuesday that 1,000 customers were hit by a similar fraud attempt.
SEB received the first indications that something was amiss about ten days ago. The bank says that hackers broke into a national computer system handling card payments for shops, hotels and other retailers.
Ottosson said that card information should never be stored by payment systems, but said in this case it had been.
"That's a criminal act, pure and simple," she said.
The card numbers allowed the frausters to buy goods over the internet and to forge new cards.
"We've seen customers already hit by such thefts. A normal customer can't protect themselves against this. But our customers will not lose out financially," she said.
All SEB customers whose card numbers might have come into the wrong hands will receive a letter from the bank asking them to block the card and order a new one.