Daku grabbed a megaphone before joining in with offensive chants about Serbia and North Macedonia after full-time in Hamburg.
Issues persist at the European Championship in Germany, with chants relating to historic political and ethnic tensions in the Balkans region.
"Daku will be banned for a total of two UEFA representative team competition matches for which he would be otherwise eligible," a statement from European football's governing body said on Sunday.
"[Daku] failed to comply with the general principles of conduct, violated the basic rules of decent conduct, used sports events for manifestations of a non-sporting nature and brought the sport of football into disrepute."
Daku has since apologised for his actions but will miss Monday's game against Spain in Dusseldorf, where Albania could book their place in the knockout stages for the first-ever time with victory.
The Albanian Football Association sent out a statement to issue an "appeal to all Albanian fans to be more responsible and avoid the creation of these totally avoidable incidents and riots".
Albania's football federation has also been fined €47,500 for lighting fireworks, a pitch invasion and transmitting provocative messages not fit for a sports event during the same match.
Meanwhile, Croatia were also penalised for lighting and throwing fireworks during the game, with UEFA issuing a €28,000 fine.
Serbia had already threatened to withdraw from the tournament over the chanting by Croatia and Albania fans at their match before the Serbia FA condemned "shameful racist behaviour" in a separate statement.
De la Fuente's side have eased through Group B, making it to the last 16 with a game to spare after beating Croatia 3-0 and Italy 1-0.
That dominance has left some comparing the current crop of Spain stars to the side that triumphed at the World Cup in 2010 and the European Championship two years later.
De la Fuente says there can be no such praise yet, however, as his new-look Spain squad have not achieved anything.
"We have a long way to go to catch up with that national team you mentioned because they won the Euros," De La Fuente said at a pre-match press conference on Sunday ahead of Monday's meeting with Albania.
"We need to improve in every area. That may seem negative but we have to keep improving. That's our goal from day to day.
"The good news is there's huge room for improvement, possibly infinite or maybe there's a limit. That's what makes us feel very optimistic."
Indeed, the triumphant Spain side from yesteryear included the likes of David Villa, Andres Iniesta and Xavi, as well as Iker Casillas and Carles Puyol further back.
Rodri has taken a Xavi-like role in midfield but will be suspended for the next clash with Albania, where De la Fuente insists Spain will not rest on their laurels.
"We're only focusing on winning because we want to win every match," the former La Roja youth coach added.
"We want to send out what we feel is the best side. We have complete confidence in our 26 players here. Everyone has a chance to play here at a high level, so I'm very calm about that."
Spain and France are the only sides to have not conceded yet at this tournament, despite the likes of England and Germany also being touted as pre-Euros favourites.
De la Fuente expects the favourites to soon click into gear, though.
"I don't think we've seen the real quality of certain teams yet," he continued. "Some of them have reached a strong competitive level straight away while others that some may call favourites or contenders, they haven't yet got going fully.
"When you head into the knockout phase, there's no room for error. So I think that once the last 16 begins, I think we'll see the real potential of every team."
Local police had informed the Albanian Football Association (AFA) that they could not guarantee the safety of the two sides for the Group I encounter at the Air Albania Stadium.
The AFA had asked for a restricted number of fans who have received a coronavirus vaccinations to be allowed into the venue, but the government refused that request.
With police having been unable to offer assurances over the safety of players outside the ground, with no lockdown restrictions in place, the AFA was concerned the fixture may have to be cancelled.
However, police released a statement later on Thursday confirming the game could ahead, saying they had "taken all measures to guarantee order and security".
The Azzurri were stunned by the fastest goal in European Championship history on Saturday as Nedim Bajrami put them behind within just 23 seconds, but goals from Alessandro Bastoni and Nicolo Barella saw them rally for a 2-1 win.
The defending champions enjoyed 68.3 per cent of the possession, created five big chances to Albania's two and recorded 34 touches in the penalty area to their opponents' seven.
However, they still had to survive a major scare at the death as Gianluigi Donnarumma turned Rey Manaj's attempted lob wide, clinching the three points.
After seeing Group B rivals Spain thrash Croatia 3-0 earlier on Saturday, former Napoli boss Spalletti knows more will be needed from Italy next time out.
"There are a number of things we still have to improve because we thought we were better than we were in too many situations," Spalletti told reporters.
"We need to be meaner. We are neat and tidy in the way we build things up, we would free up a man, but then you need to go and hurt the opposition.
"We thought we were brilliant at just keeping possession. We need to move the ball a bit more quickly, because we did so badly on occasions tonight, but against Spain there will probably be chances to play the ball forward more.
"Because they tend to be more aggressive in their bite and press, there might be greater scope to actually play in behind their defensive line."
Italy have now won their opening game on each of their last three appearances at the Euros (also 2016 and 2020), having only done so twice in their first eight (five draws, one loss).
They have also gone unbeaten through 10 games at the tournament for just the second time (seven wins, three draws), previously doing so in their first 10 between 1968 and 1988 (four wins, six draws), lifting the trophy in 1968.
