The result was Milan's second draw in the group, following a goalless match against Newcastle United, while Dortmund earned their first point of the campaign after a 2-0 loss to Paris Saint-Germain.
Newcastle are now top of the group with four points after a 4-1 win against PSG on Wednesday. Milan are third with two points while Dortmund are last.
Milan's most productive spell came towards the end of the match, but Samuel Chukwueze stumbled when presented with a clear chance, sending the ball straight to keeper Gregor Kobel, while Tijjani Reijnders put the rebound just wide.
The first meeting between the two teams in more than 20 years saw an entertaining first half.
Milan kicked off the match with a strong and high-paced performance, while Dortmund, who finished as Bundesliga runners-up last season, applied substantial pressure to disrupt the visitors' build-up and posed a constant threat on the counter-attack.
Dortmund came close several times, utilising the flanks and set-pieces to create opportunities, while Milan goalkeeper Mike Maignan made multiple saves to maintain the level score at halftime.
In the early minutes of the second half, Christian Pulisic made an attempt on goal for the visiting team, but the former Dortmund player's shot went straight to Kobel.
Milan next visit PSG on Oct. 25 while Dortmund will travel to Newcastle on the same day.
- Szymon Marciniak