The announcement is in line with the centre-right government's plan to gradually sell-off parts or all of several state-held companies.
The offer, directed to "Swedish and international institutional investors "will initially be made up of 200 million shares, with a possible extension of 55 million shares, in total representing "6.3 percent of outstanding shares in the company," the finance ministry said.
"After the transaction, the (Swedish) state's share (in Nordea) will go down from 19.8 percent currently to between 14.8 and 13.5 percent," the ministry said in a statement.
"Revenues from the sale will be used to strengthen the stability of the Swedish economy, through a reduction of the national debt," Financial Markets Minister Peter Norman said in the statement.
More details on the transaction, including on pricing, were to be made available Friday, the ministry said.
Nordea on Wednesday posted fourth quarter results above analysts' expectations thanks to the strong recovery of the Swedish economy. The bank's net profit for 2010 was €2.66 billion ($3.68 billion).
The bank counts some 11 million clients and is the largest in Sweden and in the entire Nordic region.
Swedish media reported Thursday that Finnish bank Sampo, which already holds 20 percent of Nordea, would be interested in purchasing more of the bank.
When Swedish Prime Minister Fredrik Reinfeldt's coalition first came to power in 2006, it received parliamentary backing for its plans to sell-off state-owned companies.
Sweden has already sold Absolut Vodka maker Vin & Sprit, a chunk of telecoms giant TeliaSonera, its share in the Nordic and Baltic stock exchange operator OMX and part of the postal service, among others.
Before winning re-election last September, the government reiterated its intention to let go of some or all of TeliaSonera, Nordea and mortgage lender SBAB. It has said energy company Vattenfall and its share of Scandinavian airline SAS could also soon go on the block.
Sweden holds 21.4 percent of SAS, 37.3 percent of TeliaSonera and 100 percent of SBAB.