The South Korean only resumed training last week after a month away on international duty at the Asian Cup.
“We got a blow on Saturday morning with the news that Park Ji-sung did his hamstring on Friday afternoon in training,” Ferguson said on the club's website.
“It was very unfortunate because it was his last kick of the ball in training as well.
“We were really looking forward to having him back after being away for a month at the Asian Cup. He’ll be out for up to a month, which is a blow to us.”
The injury comes at a key point in the season for United, who lead the Premier League by four points after 26 games.
Park will miss the Premier League trips to Chelsea, Liverpool and Wigan Athletic and at least the first leg of the Champions League last 16 tie against Olympique Marseille.
United visit Marseille next Wednesday before hosting the French champions in the second leg at Old Trafford on 15 March.