The Ministry of Finance said in a statement it had also named legal and economic advisers.
Analysts said SBAB is worth about 1.2-1.5 billion US dollars and will most likely go to another Nordic financial player. They cited Nordea Bank AB, Danske Bank and DnB Nor as the most likely buyers.
The center-right government won parliamentary permission last month to sell SBAB and two other state-owned firms - Absolut vodka maker Vin & Sprit and real-estate firm Vasakronon. Parliament had already approved the sale of stakes in Nordic telecoms operator TeliaSonera, the Nordea banking group, and bourse operator OMX.
In May, the government cut its TeliaSonera holding.
Morgan Stanley is financial adviser for the sale of Vin & Sprit and is now analysing options for the disposition of the 90 year-old firm amid interest from major drinks companies on both sides of the Atlantic.