His father, Jorge Messi, was also given a jail term for defrauding Spain of €4.1m (£3.5m; $4.5m) between 2007 and 2009.
They also face millions of euros in fines for using tax havens in Belize and Uruguay used to conceal earnings from image rights.
However, they are likely to avoid jail.
Under the Spanish system, prison terms under two years can be served under probation.
During the trial, Lionel Messi claimed he “knew nothing” about the management of his financial affairs, saying he was “playing football”.