Industry executives and analysts said on Monday the deal could fuel consolidation in Finland's fragmented and struggling infrastructure industry, with Austria's Strabag and Sweden's Skanska tipped as potential buyers.
"Perhaps it would have been politically difficult for the state to sell Destia directly to a foreign company," said Pohjola Markets analyst Matias Rautionmaa.
"Anyway, if the market stays like this, the players will have to come up with some kind of restructuring moves."
Destia, with annual sales of around 500 million euros, is Finland's biggest infrastructure company and competes with firms such as YIT, NCC, Lemminkainen and Skanska, as well as VR Track, another state-owned business.
The company has slashed jobs and sold assets in the last few years to shore up profitability in a weakening Finnish construction market. Last year, its core operating profit rose slightly to 19 million euros.
Its chief executive Hannu Leinonen told a news conference there was not much growth in sight without more mergers and acquisitions.
"Any growth leaps will be difficult to take without structural moves," he said.
"With the private ownership we will be able to react to the consolidation in the sector."
Ahlstrom Capital chief executive Panu Routila said it was too early to talk about future steps, but added his fund normally had an investment horizon of 5 to 7 years.
The deal, which confirms an earlier Reuters report, is part of plans by Finland's five-party government to raise about 1.1 billion euros from share sales in 2014-2015 as it looks to reduce borrowing and protect the economy's triple-A credit rating.
The government did not disclose what it might sell next, but said a large part of the sum would likely come from Solidium, its 8-billion euro investment fund for listed companies.
The fund's biggest holdings are stakes in insurance and investment firm Sampo and telecoms operator TeliaSonera.
Pressure from labour unions has limited sell-offs in recent years, and the state still owns stakes in 15 of Helsinki's top listed firms, as well as in 44 others.
(Editing by Tom Pfeiffer and Mark Potter)
By Jussi Rosendahl