Celtic Rangers and the rest of the top-flight sides will go into round four of the competition, with matches to be held on the weekend of January 22.
The fifth round will take place three weeks later on February 12, while the quarter-finals are scheduled for March 12.
The tournament then switches to the national stadium with the semi-finals on April 16 and 17. The final will take place on May 21.
Matches from the fourth round onwards will be decided on the day with no replays but instead extra-time and penalties if required.
St Johnstone are the reigning Scottish Cup holders after defeating Hibs 1-0 at Hampden Park thanks to a first-half goal by Shaun Rooney. Saints’ victory broke up Celtic’s years of domination as the Parkhead side won the competition on the previous four occasions.