The Israeli was sent off in the first half when the Parkhead side led their Danish opponents in the second round Champions League qualifier first-leg.
Bitton had picked up a yellow card prior for stopping a Midtjylland attack prior to Liel Abada opening the scoring for Celtic on his debut.
The defender clashed with former St Mirren loanee Anders Dreyer as the game headed towards half-time. Bitton squared up to the winger and jabbed a finger in his face.
It left referee Sandro Scharer with little choice but to show him a second yellow card.
The 29-year-old offered his apology after the match on social media.
He posted: “I lost my head for a second and got punished for that. Sorry again.”
Celtic were left to rue the incident despite Midtjylland going down to ten men just before the hour mark when Dreyer was given a second yellow card.
They scored ten minutes later.
“Nir had already been booked and when you’ve been booked you have to be careful in your actions,” the Australian said after the match.
"When you infringe again, you give the opportunity to the referee to give you another caution.
"It’s disappointing for him more than anything, because he was really keen to put in a strong performance. He had started really well for us, so it’s disappointing for him that he misses the second game as well.”