Both players were missing from the final 18-man squad named on Monday.
Although FIFA has ordered clubs to release all under-23 players who are selected for the event, Shaqiri last week said his priority was to win a place in the Bayern Munich starting line-up and he would prefer to stay with his club.
The Swiss Football Federation (SFV) had initially said that Xhaka, a cultured midfielder, would take part in the Games.
But on Sunday, Xhaka's club Borussia Monchengladbach said they had agreed with the SFV that the player would stay with them to prepare for a Champions League qualifying tie in late August.
He has been replaced in the squad by FC Zurich's Oliver Buff.
Xhaka and Shaqiri were both instrumental in helping FC Basel reach the last 16 of the Champions League last season, eliminating Manchester United in the process.
Switzerland were also thwarted in their hopes of fielding Valon Behrami as one of three permitted overage players after Fiorentina declined to release him.
Xavier Hochstrasser was included instead.
Squad:
Goalkeepers: Diego Benaglio (VfL Wolfsburg), Benjamin Siegrist (Aston Villa)
Defenders: Francois Affolter (Werder Bremen), Fabio Deprela (Brescia), Timm Klose (Nuremberg), Michel Morganella (Palermo), Ricardo Rodriguez (VfL Wolfsburg), Fabian Schaer (FC Basel)
Midfielders: Amir Abrashi (Grasshoppers) Oliver Buff (FC Zurich), Fabian Frei (FC Basel), Xavier Hochstrasser (FC Lucerne), Pajtim Kasami (Fulham), Alain Wiss (FC Lucerne)
Forwards: Josip Drmic (FC Zurich), Innocent Emeghara (Lorient), Admir Menmedi (Dinamo Kiev), Steven Zuber (Grasshoppers).
