The hosts have only just ended a lengthy losing run, while Frankfurt look set to be Bayern Munich's closest challengers for the Bundesliga title this season.
Match preview
History beckons for Frankfurt this week, because they could equal an all-time Europa League record if they avoid defeat in Denmark.
The current record for the longest unbeaten run stands at 18, set by Chelsea between 2013 and 2019, but Frankfurt are now just one shy of equalling that streak, following an unbeaten start.
Frankfurt were last in the competition when they won it during the 2021-22 season, and are rightfully among the favourites to do so again under Dino Toppmoller, being one of eight clubs yet to suffer defeat at the halfway stage of the league phase.
It is not just in Europe where Frankfurt have been excellent too, because they have lost just one of their last 15 matches in all competitions, and that was against reigning champions Bayer Leverkusen.
Die Adler recorded a fifth straight win at the weekend, beating Werder Bremen 1-0 to pick up where they left off before the international break, moving them into second, six points behind Bayern.
In that five-game winning run alone, there have been a few eye-catching results, including a 3-2 success at Stuttgart, as well as a 7-2 thrashing of Bochum.
Toppmoller's men also beat Borussia Monchengladbach to reach the last 16 of the DFB-Pokal, and a matchday four win over Slavia Prague in this competition means they are one of a cluster of sides breathing down the neck of Lazio in first place.
Four of those five recent wins have come at home, but they have proven they are competent travellers too, winning four of their last six on the road.
It has been a while since they faced Danish opposition in Europe though, with the last meeting coming all the way back in the 2006-07 season against Brondby, and a draw on that occasion extended a fine record of just one defeat in six games against clubs from the country.
Midtjylland are in a good position at the halfway mark, sitting 13th, comfortably inside the qualification places, and just two points off the top eight.
Form of late is of great concern though, because a narrow 1-0 home win over Silkeborg on Monday was required to end a four-game losing run for Thomas Thomasberg's men.
Some results in that streak were very concerning too, including a 5-1 home thrashing at the hands of Brondby, and a 2-0 defeat in Bucharest against FCSB on matchday four, which saw goalkeeper Elias Olafsson comically kick the ball at opposing striker Daniel Birligea for a goal just six seconds into the second half.
Those results saw them concede top spot in the Danish Superliga to Copenhagen, and ended their unbeaten start in Europe, which had begun well, and a run of eight games unbeaten on home soil on the continent should provide some belief they can get back on track.
Having scored just two goals in their last five matches suggests they may struggle though, especially given the level of opposition they are facing - a class above the only other German side they have faced in Europe, Hoffenheim, on matchday one this season.
FC Midtjylland Europa League form:
D
W
W
L
FC Midtjylland form (all competitions):
W
W
L
L
L
W
Eintracht Frankfurt Europa League form:
D
W
W
W
Eintracht Frankfurt form (all competitions):
D
W
W
W
W
W
Team News
The only confirmed absentee for the hosts is set to be Chilean striker Dario Osorio, who has now missed the last two games, and was not available for his nation during the recent international break.
Many players are closing in on a return though, including Christian Sorensen, who should return from illness, as well as Cho Gue-sung and Marrony, from respective knee injuries, but it is unclear when Franculino and Aral Simsir may return.
Frankfurt will be without full-back Rasmus Kristensen, who will miss the chance to return to his homeland here due to a thigh injury, while fellow Dane Oscar Hojlund is also absent and will not return until next month.
Sasa Kalajdzic's long road to recovery from another ACL tear will keep him sidelined until 2025, and Aurele Amenda's ligament injury has him ruled out until February.
Omar Marmoush suffered the rare feeling of not finding the net in the weekend win, after scoring in four straight games prior, but the Egyptian has been used in this competition as well as for domestic matters, and has two goals plus an assist in the league phase so far.
FC Midtjylland possible starting lineup:
Olafsson; Mbabu, Diao, Bech Sorensen, Andersson; Castillo, Martinez, O Sorensen; Byskov, Buksa, Gogorza
Eintracht Frankfurt possible starting lineup:
Trapp; Collins, Tuta, Koch, Theate; Knauff, Dahoud, Larsson, Gotze; Uzun, Marmoush
We say: FC Midtjylland 1-3 Eintracht Frankfurt
Midtjylland have been struggling of late, both offensively and at keeping goals out of their own net, so may struggle against a ruthless Frankfurt side that have been sweeping everybody aside with little fuss recently.