United will be at home in the second leg which is due to take place on 5th March, with Solskjaer's men travelling to Austria one week earlier.
5-time winners Sevilla have been handed a tough tie against Italian giants Roma, while Inter Milan will face La Liga surprise package Getafe.
Rangers will face German outfit Bayer Leverkusen. Steven Gerrard's men are at home in the first leg. Olympiacos' reward for defeating Arsenal is a tie against fellow English side Wolves.
Ties will be played on 5th and 12th March.
Complete last 16 draw:
Istanbul vs Copenhagen
Olympiacos vs Wolves
Rangers vs Leverkusen
Wolfsburg vs Shakhtar
Inter vs Getafe
Sevilla vs Roma
Frankfurt/Salzburg vs Basel
LASK vs Manchester United