The allegations originate from 2013 and 2014 when prosecutors alleged that Kinnunen made false income tax and VAT declarations on behalf of a company for which he was a board member.
He also faced charges over flawed accounting related to the issue of falsified invoices.
The total value of the fraud was believed to have amounted to some SEK 700,000.
Kinnunen has always maintained his innocence.
He withdrew as an MP for the right-wing Sweden Democrats, although the party leadership supported him throughout the affair.
The company where the alleged offences were believed to have been committed has close links to the Sweden Democrat party.
If he had been found guilty, Kinnunen would have faced a jail term of up to six years.