United, knocked out of the Champions League last week, meet the Danish league winners, an unsung club backed by owner Matthew Benham who eliminated Southampton earlier in the competition.
Midtjylland's pony-tailed chairman Rasmus Ankersen, appointed by former financier and professional gambler Benham, who also owns English second-tier club Brentford, issued a warning after the draw.
"We have already beaten one English team so we are not afraid," said Ankersen. "We are a small club with a small budget and we know we can't outspend them so we have to out-think them and, so far, this way has worked for us in the Europa League.
"We know we have a chance and we will take up the challenge. If we can beat Southampton we can beat Manchester United and the players will feel that and believe it."
Midtjylland have adopted the use of mathematical modelling and key performance indicators in their management and style of play, factors Van Gaal will need to study after a probable call to fellow Dutchman and Southampton manager Ronald Koeman.
Van Gaal has received a lot of criticism following his team's Champions League exit and their 2-1 defeat by promoted Bournemouth in the Premier League on Saturday.
In other eye-catching ties Liverpool manager Juergen Klopp returns to Germany to face Augsburg, who are in their maiden European campaign, while Sevilla, bidding for a hat-trick of Europa League titles, meet Norwegian team Molde.
Former Champions League winners Borussia Dortmund and Porto also lock horns while Olympique de Marseille take on Athletic Bilbao, Anderlecht play Olympiakos Piraeus, Shakhtar Donetsk face Schalke 04 and Lazio meet Galatasaray.
The first legs will be played on Feb. 18 and the return matches seven days later.
(Makes clear Augsburg but not Midtjylland are in maiden campaign)
(Writing by Tim Collings; Editing by Tony Jimenez)
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