Federation Internationale de Football Association announced later Sunday it had opened disciplinary proceedings against Slavisa Kokeza, who is president of the Serbian FA, and coach Mladen Krstajic for post-match comments.
After falling behind in the fifth minute, Switzerland defied a cauldron-like atmosphere created by fervent Serbian supporters as they hit back with a thunderbolt from Xhaka and a last-minute breakaway goal from Shaqiri.
Despite being recognised by UEFA, Serbia does not acknowledge Kosovo as an independent state, with relations between the Balkan nations remaining tense.
Xhaka's brother plays soccer for Albania's national team.
Both players celebrated with the gesture of the double eagle, which appears on the national flag of Albania - a country with which Serbia has a turbulent and troubled past.
They also have complained that Brych showed four Serbia players yellow cards but only one Swiss player was booked.
But there were earlier cases before Shaqiri and Xhaka's.
Switzerland's Xherdan Shaqiri celebrates scoring their second goal during the World Cup group E match between Serbia and Switzerland in Kaliningrad Stadium in Kaliningrad, Russia, on June 22, 2018. I'm very happy to score this goal.
Both the Switzerland and Serbia teams played down any political factors before the game last Friday.
He said: "I don't have any comment. My celebration was for the people who have always supported me".
"You should never mix politics and football".
Meanwhile, the Serbian papers also slammed what they labelled "shameful provocation" by Shaqiri and Xhaka.
Serbia has refused to recognize Kosovo's independence, which was won after North Atlantic Treaty Organisation intervened militarily in 1999, launching airstrikes against Serb forces battling separatists in the province and bombing targets as far away as the Serbian capital, Belgrade.
The build-up to the match had seen exchanges between Serbian players and Shaqiri, who wears boots with the Kosovo flag displayed on one heel and the Swiss one on the other. Kosovo is mostly populated by Albanians.