Both players are ethnic Albanians from Kosovo, where a Serbian crackdown on the Albanian population only ended with Nato military intervention in 1999.
After scoring, they made an eagle gesture in a symbol of the two-headed eagle on the Albanian flag.
Both were booed by Serbia fans.
In a statement, Fifa said its disciplinary committee had opened proceedings against Xhaka and Shaqiri, adding: "In relation to the same match, disciplinary proceedings have been opened against the Serbian FA for crowd disturbance and the display of political and offensive messages by Serbian fans.
"Furthermore, a preliminary investigation has been opened against the coach of the Serbian national team, Mladen Krstajic, for alleged statements made in the aftermath of the said match."
It is unclear what the investigation into Krstajic refers to, but in comments to Serbian reporters on Saturday, he said of match referee Felix Brych: "I wouldn't give him either a yellow or red card, I would send him to The Hague. Then they could put him on trial, like they did to us."
Serbia accuse Fifa of 'brutal robbery' at World Cup
'Double eagle' celebration provokes Serbs
After the game, which his side won 2-1, Switzerland's Bosnia-born manager Vladimir Petkovic was asked about the celebrations and said: "You should never mix football and politics. It's important to be a fan, and to give respect.
"It was a wonderful atmosphere and that's what support should be about."
Xhaka's father spent three and a half years as a political prisoner in Yugoslavia while Shaqiri was born in Yugoslavia before emigrating to Switzerland as a child.
Shaqiri also sported a Kosovan flag, stitched onto his boots.
"It's just emotion," he said about his celebration. "I'm very happy to score this goal. It's not more. I think we don't have to speak about this now."
for more read please visit on https://www.bbc.com/sport/football/44586681
or http://www.whispereye.com/2018/06/24/world-cup-2018-fifa-investigates-switzerland-duo-over-goal-celebrations/