The 26-year-old Rubin Kazan forward insulted North Macedonia and later apologised for it, but will now miss his side's final Group B match against Spain on Monday and a potential last-16 clash.
"Daku will be banned for a total of two UEFA representative team competition matches for which he would be otherwise eligible," said European football's governing body in a statement.
It said the punishment was for "failing to comply with the general principles of conduct, for violating the basic rules of decent conduct, for using sports events for manifestations of a non-sporting nature and for bringing the sport of football into disrepute."
With one point after two matches in Group B, Albania face likely elimination from the Euros unless they beat Spain in Duesseldorf on Monday.
If they are eliminated in the group stage, the second game of Daku's ban will be carried over to the start of the UEFA Nations League in September.
"He knows he made a mistake. He has apologised, and now we need to think about tomorrow's match," Berat Djimsiti, the Albania captain, told reporters on Sunday in Dusseldorf.
"I am not here to talk about politics. That is up to UEFA."
Daku had been introduced as a substitute five minutes from the end of Wednesday's 2-2 draw with Croatia in Hamburg. He didn't play at all in his team's opening 2-1 loss to Italy.
"We are here to play football in a major tournament. We are here to talk about football," said Sylvinho, Albania's Brazilian coach, when asked about the ban.
"There is not much to say. We can't waste energy on anything other than preparing for tomorrow's game."
UEFA also handed the Albanian Football Association fines totalling 47,500 euros ($50,787) for several offences related to the Croatia game.
Of that, 25,000 euros was for "transmitting provocative messages not fit for a sports event", 20,000 euros was for invasions of the pitch, and 2,500 euros was for the lighting of fireworks.
UEFA said investigations into potential racist or discriminatory conduct by supporters in the Croatia match were "ongoing".
Serbian Football Association chief Jovan Surbatovic had called for sanctions after claiming supporters had struck up chants hostile to his country.
