Zambia international Saka suffered the setback during Leicester's final pre-season friendly with Lens and has now undergone surgery, Cooper said, adding Jamie Vardy and Conor Coady were set for spells on the sidelines as well.
"Patson is not great," said Cooper ahead of his side's Premier League opener at home to Tottenham on Monday. "He's suffered quite a serious ankle injury.
"He's had an operation and will be out for a few months. Vards has been injured since the second week of pre-season, he's closer to returning but will be a little while.
"It's not great. Conor Coady will be out for a few more weeks with his hamstring.
"Vards is at the latter stages of rehab. With his experience, he understands his body and will have a big say in that process of returning."
Leicester also have the threat of a points deduction hanging over them for alleged breaches of the Premier League's profit and sustainability rules, with the Foxes having no plans to sign new players before Monday's match with Spurs -- their first fixture since returning to English football's top flight.
"Every season you want to reinforce, you want to strengthen," said Cooper. "We're still going through that process. The club is working together and the communication lines are great.
"It's been a slow market. Once I knew this week that there wouldn't be any additions for Monday, I put that to one side and focused on Monday. That's the only thing we can influence," he added.