The midfielder suffered a muscle strain in Sunday's 3-0 Carabao Cup final victory over the Gunners at Wembley.
City are uncertain how long the 32-year-old will be out of action but they will not risk his involvement at the Emirates Stadium this week.
"Scans have shown Fernandinho suffered a hamstring strain during the Cup victory over Arsenal," City said in a statement.
"The Brazilian was withdrawn after 52 minutes of City's Wembley win, but thankfully the initial prognosis suggests the problem isn't serious.
"No timescale has yet been set for his return but the Premier League game against the Gunners on Thursday will come too soon."
Top-of-the-table City head into the match looking to stretch their lead over second-place Manchester United back to 16 points.