The pair were left behind as Pep Guardiola’s side flew out for Wednesday’s round of 16 first-leg tie in Germany.
Stones is recovering from a groin strain, while Jesus has a hamstring problem – but both are expected to recover in time for Sunday’s League Cup showdown with Chelsea at Wembley.
Benjamin Mendy, who is still working his way back to full fitness after a meniscus injury, also stayed behind, despite returning to training this week.
Fabian Delph was also absent from City’s travelling squad.
But Vincent Kompany is in contention to take part against Schalke after more than a month on sidelines.
Guardiola couldn’t disguise his frustration when assessing his latest injuries in the middle of such a hectic run of games as City pursue an unprecedented quadruple.
City are set to head to China and possibly Japan during the summer.
There was more than a hint of sarcasm in Guardiola’s tone when he added: “We’ll come back and play in China to play the big clubs in Europe, and we have to win because if we don’t win the season will be a mess.
Schalke vs Manchester City predicted line-ups
Schalke (3-4-3): Fahrmann; Nastasic, Oczipka, Sane; McKennie, Serdar, Bentaleb, Harit; Uth Matondo, Kutucu
City (4-3-3): Ederson; Walker, Otamendi, Laporte, Zinchenko; Fernandinho, De Bruyne, D Silva; Sterling, Aguero, Sane