The 30-year-old former England midfielder joined City this week in the hope of reviving his career after being released by Manchester United.
But after making just four appearances for United during an injury-plagued past three seasons, City have decided not to include him among the 17 unrestricted places they had available in their Champions League squad.
The other eight places in a group of up to 25 must be reserved for homegrown or locally-trained players.
Hargreaves' absence means he will miss two Group A games against another of his former clubs, Bayern Munich, as City enter the competition for the first time.
Manager Roberto Mancini, however, will have the chance to review his squad in January should City progress to the knockout stages.
Hargreaves himself has accepted he needs time to build up his fitness, telling City TV on Thursday: "It's important that you get back into a rhythm of playing football, and I haven't done that for a while.
"There's tons of games to come this season in various competitions."
City, who also play Napoli and Villarreal during the group stages, have named just 23 players in their squad having opted not to use two of the spots earmarked for their own Academy players.
Kolo Toure is included after completing his six-month ban for failing a drugs test as is Carlos Tevez, whose sought-after summer move failed to materialise.
Former England defender Wayne Bridge is not named but Mancini has already made clear the left-back does not feature in his plans.