Banners have been prepared by some of the 800 fans attending the game at the 11,800-capacity MCH Arena.
One of them, created by Thomas Kearney, has 'WELCOME TO SCAMDINAVIA' written on it in black and white letters.
It highlights the fact that United fans have been charged $140 per ticket whereas Southampton supporters were charged just $44 when they played at the home of the Danish champions in the Europa League play-off round in August.
United fans are expected to sing about their annoyance at the ticket charge during the game on Thursday.
"£71 to watch a Europa League game is extortionate," said Andy Mitten, author and editor of fanzine United We Stand.
"The combined cost of all three tickets for Manchester United's Champions League away games was only £75.
"Do they think United fans are three times wealthier than Southampton fans? Midtjylland are ripping fans off - their own and the 800 travelling fans."
Given that fans will have to pay up to $200 to reach Herning and hotels are charging up to $640 for a room, a two-night trip to Denmark could cost well over $2,000.
"Many fans go to great extremes to work out the cheapest ways to organise trips and to then get clobbered like this on ticket prices is a real slap in the face," said Duncan Drasdo, CEO of the Manchester United supporters' trust.
"I feel that UEFA - and similarly the FA & Premier League - should protect away fans as a special case by requiring that in addition to away fans being charged no more than home fans in equivalent seating they should also outlaw 'away categorisation', so that away fans of all clubs should be charged the same lowest price in the same competition in the same season.
"Clubs need to accept that they are not selling tickets in a normal competitive market as fan loyalty means each club is an effective monopoly so they shouldn't be applying normal supply and demand economics. They wouldn't be able to do this in other industries - banking, utilities etc where prices are regulated because the market is not operating efficiently."
FC Midtjylland failed to respond to requests for a comment on Tuesday.