Manchester United will take on Wolverhampton Wandereres in the FA Cup quarter-final ties with a place at Wembley.
Solskjaer will now take on Premier League surprise package Wolves, who have already taken points off several top-six sides this season.
Premier League champions Manchester City will be in action against Championship outfit Swansea, while Crystal Palace travel to Watford.
The quarter-finals for the FA Cup will take place from 15-18 March, with the clubs who emerge victorious sharing £720,000 in prize money. The semi-finals, meanwhile, will take place on the weekend of April 6 at Wembley.
The FA Cup quarter-final draw in full
Swansea City v Manchester City
Watford v Crystal Palace
Wolves v Manchester United
Millwall v Brighton