The bank denied any wrongdoing and said it would appeal the demand.
"The review relates to transactions that were carried out before a change in Germany's tax legislation came into force in 2016. SEB is of the opinion that these were carried out in accordance with then prevailing rules," it said in a statement.
SEB said in a separate statement that Germany's public prosecutor had on Dec. 14 and 15 visited the bank's office in Frankfurt and requested information on alleged cum-ex transactions. The bank said it was cooperating with authorities.
"To the best of our knowledge, SEB in Germany has not offered or conducted transactions where the purpose is to recover tax that was not paid. We distance ourselves from that type of arrangement," it said, describing the cum-ex scandal.
The scandal is potentially Germany's biggest post-war fraud involving a share-trading scheme, which authorities say cost taxpayers billions of euros.
It is the subject of multiple investigations involving numerous financial institutions across Germany as the government tries to claw back money it says was stolen from the state.
German prosecutors in Cologne said in a statement a raid was conducted in Frankfurt, but declined to name the bank involved.
SEB said it had, in accordance with current accounting rules, made no provisions at a group level related to the matter. It also said further demands could not be ruled out and that this could have a negative financial impact on the bank.
SEB said that, including the latest order, Germany's tax authority had demanded a total of 936 million euros relating to alleged ex-cum transactions, and that legal proceedings were expected to take several years.
SEB said last year the tax authority had requested its German subsidiary DSK Hyp AG to retroactively repay "transparently reported withholding tax" from more than five years ago, adding it strongly opposed the decision.
($1 = 0.8882 euros)
(Reporting by Johan Ahlander and Helena Soderpalm; Editing by Niklas Pollard and Mark Potter)
By Johan Ahlander and Helena Soderpalm