Star frontman Ibrahimovic was forced off during the second half of Wednesday night's first leg at the Parc des Princes, where the French champions beat their Premier League opponents 3-1 to seize a commanding lead to take to London.
The major setback for the Swedish striker and his club was announced by PSG president Nasser Al-Khelaifi on French radio station RMC on Thursday.
Al-Khelaifi said on Thursday afternoon: "He is doing an MRI now. I think he will need a minimum of four weeks (out of action)."
Asked if there was any chance he could play on Tuesday at Stamford Bridge, Al-Khelaifi said: "It's impossible."