Dortmund forward Karim Adeyemi was brought down in the box by Bochum defender Danilo Soares midway through the second half on Friday night, with the scores locked.
Referee Sascha Stegemann waived play on and declined to use the VAR system to review the contact.
The German FA's referee department said on Saturday "the TV pictures prove" the incident was "a foul and a penalty."
"The defender throws himself from behind to the side with both legs and did not compete for the ball.
"He (Soares) does not play at the ball and instead hits the opposing player, knocking him down".
Dortmund manager Edin Terzic said after the match the decision was a "key moment" in the draw, which gave Bayern Munich an opportunity to go first with a win against last-placed Hertha Berlin on Sunday, with four matches remaining.
Dortmund sporting director Sebastian Kehl said after the game "today, the referee decided the outcome of the match."
"With the German championship at stake, to not look at this situation, is negligent, cowardly and completely wrong."
Soares was already on a yellow card and would likely have been sent from the pitch with a second booking, should the play have been reviewed.
The German FA's refereeing boss said the decision could have been made in favour of Dortmund "without the need for video assistance."
The statement also commented on a late decision not to award a handball against Bochum, saying "the decision of the referee was understandable."
Bayern have won the last ten German titles in a row.
