Foreign Minister Erkki Tuomioja said the "serious and extensive" hacking of the ministry's computer system was detected and halted in the spring, The Wall Street Journal reported.
He addressed the matter after Finnish media reported the network had been breached for up to four years.
Tuomioja said a case of "serious" espionage was being investigated, RIA Novosti reported.
Tuomioja said the Finnish Security Intelligence Service investigated the hacking, but did not identify potential suspects.
"We have no evidence to make public and unequivocal allegations against anybody," he said.
Russia and China did not comment on the accusations.
Tuomioja said that the hacked network wasn't used for "the most sensitive" communications, the Journal said.
The minister said no classified information was leaked because it was on a separate system.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Exploding whale video goes viral on Internet