The gunman had opened fire around 1:53 am (2253 GMT) from a rooftop in the centre of Hyvinkaa, a city about 50 kilometres (31 miles) north of the capital Helsinki, killing a 18-year-old woman, local police said in a statement.
He also wounded eight others, including a man also aged 18 who later died in hospital from his injuries, according to Finnish news agency FNB which quoted police.
Police did not identify the suspect, but said he was dressed in camouflage fatigues. He did not have any previous criminal records, nor did he resist his arrest close to Hyvinkaa.
Police added that the suspect was not in possession of any gun permits.
AFP