The country's security service, the SBU, said it had obtained data that points to a link with an attack on the nation's capital, Kiev, in December.
Ukrainian firms were among the first to report issues with malicious software on Tuesday, before the virus spread.
Moscow denied any involvement, adding that the allegations were "unfounded".
The virus, which disrupted IT systems across the globe, froze computers and demanded a ransom be paid in the digital currency Bitcoin, which is untraceable.