The former Chelsea forward is charged with defrauding the state of more than €1 million (£813,000) by not declaring payments of more than €5.15m (£4.19m) from his 2014 move to Stamford Bridge.
It is also alleged that the Spain striker, who was born in Brazil, failed to declare €1m in image rights.
Prosecutors in Madrid want the 31-year-old to be given a six-month prison sentence, while he could also be hit with a fine of €507,208 (£457,128).
Sentences up to two years for non-violent crimes can be exchanged for fines in Spain, so Costa will not spend any time in jail if convicted, but he could be forced to pay out an additional €36,500 (£32,896).
Costa has managed just 19 appearances and two goals in an injury-hit season so far for Atleti, but will be expected to feature more when LaLiga returns next month.