The 20-year-old was forced to sit out the Buddies' 2-2 draw with Inverness on Boxing Day.
But he is expected to return in time for the club's Scottish Communities League Cup semi-final against Celtic at Hampden Park on 27 January.
"He goes in for a minor operation. It also falls into the period going into the winter break," St Mirren boss Danny Lennon told BBC Scotland.
McLean has scored six goals in 22 appearances for St Mirren this season and has been linked with a move to Nottingham Forest or Ipswich.