He will miss this weekend's trip to Southampton, but there is a chance he will be available for the clash against Everton at the Etihad Stadium next week.
Dzeko has been sidelined with a calf problem for a few weeks but won't return for this weekend's trip to St Mary's to take on second-place Southampton.
City will still be without David Silva and Aleksandar Kolorov for the trip to the South coast on Sunday lunchtime.
Pellegrini told reporters at his press conference: "I suppose Edin will be fit next week... there are no complications with Silva, it was a ligament injury and he is recovering."
City face a trip to the Stadium of Light to take on Sunderland in midweek before they face Everton at the Etihad Stadium next Saturday, which could be pencilled in for Dzeko's return.
The Chilean was also full of praise for Sergio Aguero given his heroics against Bayern Munich in midweek, and has praised the spirit of his side after coming from behind to win against both Bayern and Swansea City in the past week.
He added: “We can't complain about our spirit. We were losing against Swansea and we scored twice – the same against Bayern."
Pellegrini has also said he is not surprised by the start to the season that Southampton have made - with Ronald Koeman's side currently second going into this weekend's game, after a summer which has seen the side transformed a great deal.
“Southampton are a good team with very good players and they’re playing very well. It’s no surprise they are where they are.
"Koeman has lost four or five players but they are still a good team and that’s a merit to him. It will be a tough game."