Ange Postecoglou will kick off his Hoops reign when the Danes visit Glasgow on July 20 or 21 before the return trip to the MCH Arena a week later.
But that gives the former Yokohama F. Marinos head coach just five weeks to shape his squad.
Midtjylland came up against Rangers in Europa League qualifying in 2019, losing 7-3 on aggregate, but did hammer Slavia Prague 4-1 last season en route to the Champions League group stages, where they drew with Liverpool.
Meanwhile, Hibs will face either Mons Calpe of Gibraltar or Andorra’s Santa Coloma in the inaugural Europa Conference League second qualifying round.
Aberdeen were drawn to play Sweden's BK Häcken.
The two-legged ties will be played on July 22 and 29, with both Scottish sides at home for the first leg.