PSG gave no reason for the omission of France's captain but 24-year-old Mbappe is refusing to sign a new contract.
His omission will fuel fresh speculation that he could leave to join Real Madrid before next season.
The forward declared in May that he did not want to extend his PSG contract, which expires next year, but indicated he wanted to remain at the club for a final season.
"I still have a year left on my contract and I am going to honour my contract," he said.
That would allow him to become a free agent next summer and leave PSG for nothing, a prospect that club president Nasser al-Khelaifi said was "impossible".
"We can't let the best player in the world today leave for free," Khelaifi said.
Khelaifi even gave Mbappe an ultimatum of a "maximum two weeks" to make his decision -- sign a new contract or leave this summer. That date corresponds roughly with the departure of the team for Asia on Saturday.
When training resumed on July 15, Khelaifi again asked the Mbappe camp to clarify the situation. But he has not received a response, a source with knowledge of the negotiations told AFP.
Mbappe has been taking part in the club's pre-season preparations and played the last 30 minutes and scored as PSG entertained Le Havre in a training ground friendly on Friday.
Mbappe, the club's all-time top scorer with 212 goals in 260 appearances, remains the second most expensive player in history.
He was still a teenager when he joined PSG on a season-long loan from Monaco in August 2017.
The move turned into a permanent transfer the following year in a 180-million-euro ($200 million) deal.
The 29-player PSG squad that flies east will include Mbappe's younger brother, 16-year-old Ethan Mbappe, as well as Neymar, the Brazilian whose transfer fee of 222 million euros in 2017 is the world record.
- Madrid bound? -
In a letter PSG sent to Mbappe on July 5, the club expressed a feeling of betrayal, saying it had "helped you" and "supported your family since you were a teenager".
The club said Mbappe was not choosing the "win-win" solution -- extend and not leave for free or accept a transfer.
"This is how all the great players, like you, left their club," PSG wrote in their July 3 letter to the player.
The club is convinced that Mbappe has already agreed to join Real Madrid for free in June 2024, with the promise of a staggering signing bonus, since the Spanish giants would have saved on the transfer.
A source involved in the negotiations insists that PSG have already received a 300-million-dollar offer from Saudi Arabia for Mbappe although it is considered unlikely he will go there.
Mbappe was expected to leave a year ago for Real Madrid when his previous contract came to an end, only to agree a new deal to remain in Paris.
Having missed out on his signature a year ago, Real would again be chief among his suitors.
They are in the market for a new forward after reigning Ballon d'Or Karim Benzema ended his 14-year stay in the Spanish capital, opting to move to Saudi Arabia.
Mbappe helped France to World Cup glory in 2018 and has established himself as arguably the leading attacker on the global stage.
He scored a hat-trick in France's World Cup final defeat last December to Lionel Messi's Argentina before helping PSG win a record 11th French title.
He was the top scorer in Ligue 1 last season with 29 goals and netted 41 in 43 games for his club in all competitions.
PSG are under new management, with Luis Enrique as coach.
Their Asian tour opens against Cristiano Ronaldo's Saudi club Al-Nassr in Osaka on Tuesday.
PSG then play Cerezo Osaka, also in Osaka, and Inter Milan in Tokyo before finishing off the tour in Busan, South Korea, against Jeonbuk Motors on August 3.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)