The home side had a terrible start to the match with their rearguard looking very vulnerable in the opening stages.
And the Danes were duly punished after seven minutes, when Jamie McGrath took the chance with a direct free-kick from a tight angle and surprised keeper Jonas Lössl, who saved the effort but the ball had already crossed the line.
The goal woke up the Danes who managed to put pressure on the away team for large parts of the first half, but lacked composure to make the most of their opportunities.
The attacking duo of Franculino and Adam Buksa did both have chances to restore parity, but lacked sharpness in the decisive moments.
FC Midtjylland's Franculino had the best Danish chance of the half during a counter attack but blasted the ball over the bar from the edge of the box.
Shortly before the end of the half, Martin Boyle thought he had doubled the lead for the Scots, but after a VAR-check, the goal was ruled offside.
In the second half, the home side launched a virtual siege on the Scottish goal but struggled to make their dominance tell against a resilient Scottish rearguard.
But the Danes did manage to score a crucial equalizer with about twenty minutes to go from a set piece, when Aral Simsir curled the ball into the near corner beyong the reach of Hibs keeper Jordan Smith to silence the away supporters.
With the Scots looking tired, the Danes pressed on for the all-important match-winning goal and did manage to carve out a great chance for Kevin Mbabu but as he failed to capitalize on the golden opportunity, FC Midtjylland were left to settle for a 1-1 draw.