BayernLB will give more details of the complaint at a press conference in Munich on Thursday, it said in a statement.
Austrian Chancellor Werner Faymann told reporters in Vienna he hopes Austria will win in court.
Alfred Autischer, a spokesman for Hypo Alpe, said he didn’t know about the lawsuit, which was first reported in the German newspaper Süddeutsche Zeitung.
"We cannot accept this expropriation," Bavarian Finance Minister Markus Söder told the paper.
Earlier this year Austria introduced a special law that imposed losses on holders of €890 million euros ($1.1 billion) of Hypo Alpe’s state-guaranteed debt.
The same law also voided €800 million of loans owed to Munich-based BayernLB, which acquired a majority stake in the lender in 2007.
Hypo Alpe was nationalized by the Austrian government in 2009 to save it from collapse, after it took on bad loans in the former Yugoslavia.
BayernLB said in June that it would take “all necessary measures” to protect its position.
Other investors hit by the law - including insurers Uniqa and Vienna Insurance - have also said they will take legal action, but a court spokesman in Vienna said it had not received any such actions so far.
Hypo Alpe is in the process of selling its profitable units and converting the rest into a “bad bank” that won’t have to adhere to stricter bank capital rules.