The 27-year-old suffered the injury during his side's recent 12-39 defeat at home to Warrington Wolves.
McDonnell is not expected to recover in time for next month's Grand Final, should the Saints get that far in the playoffs.
"He doesn't require surgery so it's a six-week injury," coach Nathan Brown is quoted as saying by Sky Sports News. "It's on the best side of what we could expect."
The Saints play their final match of the regular season on Friday with a trip to Huddersfield Giants.