Spanish striker Alvaro Negredo had already been ruled out with a broken foot.
"Frank Lampard is not ready to play," Chilean Pellegrini said.
"All the players that arrive this Monday, Demichelis. Vincent Kompany, Pablo Zabaleta, Sagna, Fernandinho, Lampard and Aguero, they have a special pre-season this week and next week.
"Negredo has at least two or three months that he won’t play. He is coming to Carrington again and he is working on different things."
Pellegrini said beating last season's FA Cup winners Arsenal was important for setting the right tone for the defence of their league title.
City suffered surprise defeats to Cardiff City and Aston Villa early on last season, and while they eventually fought their way to the Premier League summit, Pellegrini was keen to avoid a similarly slow start.
"It is not a friendly match," he added.
"It is an important game against an important team in Arsenal.
"Maybe both teams, Arsenal and our team, do not arrive in our best moment because both have a lot of players who have just arrived from the World Cup but I think it will be a very good game and important for both teams to win it.
"We have to start from zero, we won the title last year but now plenty of teams have the same option."
Arsenal will be without their three German World Cup winners - Mesut Ozil, Per Mertesacker and Lukas Podolski.
(Reporting by Josh Reich, editing by Pritha Sarkar)
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