Belgium international Dembele appeared to eye-gouge forward Costa during Spurs' 2-2 draw with Chelsea on Monday.
Referee Mark Clattenburg did not punish the 28-year-old during the game.
Dembele chose not to contest the charge, and will now be unavailable to manager Mauricio Pochettino until Spurs' fifth game of next season.
He has made 29 appearances in the league this season, scoring three goals.
Dembele was one of nine Spurs players booked in the draw at Stamford Bridge - a Premier League record for one team.