The Bavarians will have the harder path facing Italian champions Juventus on April 2nd, while BVB play Spanish debutantes Malaga the following day.
While Munich have the pleasure of a home advantage for the first leg of the tie, Dortmund travel to their opponents' home turf in southern Spain and will play host for the second leg.
"This is no dream tie. We will need two good days to reach the semi-final. It will not be a walk in the park, I assure you," said Bayern chairman and former player Karl-Heinz Rummenigge.
"Malaga is a good draw, especially as the first leg is away. I'm looking forward to it. I think we can do it," Borussia Captain Sebastian Kehl said.
Four-time winners Barcelona have been drawn against Paris Saint-Germain, with recent signing David Beckham in their ranks, while Spanish league-leaders Real Madrid face Galatasaray Istanbul, who put Schalke 04 out of the competition in a narrow win on Tuesday.