The 22-year-old was presented to the press as a PSG player on Friday, just three days after his last appearance for Monaco against Valencia.
But the left-back said: "I need treatment for eight to 10 days."
Kurzawa, who initially injured his right ankle in February, is expected to provide competition to Brazilian Maxwell for a starting berth at left-back.
"I've come here to play as much as possible," said the twice-capped France international, who signed a five-year deal with PSG.
"Maxwell is here, there will be competition, the best will play."
Kurzawa will not make an instant return to the Stade Louis II on Sunday but could make his PSG bow two weeks from now following the international break.