The match, the first of two legs between the two sides in Europe's premier club competition, has been called off until tomorrow.
Stadium spokesman Norbert Dickel informed fans of the cancellation, saying that "there is no reason for panic here at the stadium."
North Rhine-Westphalia police spokesman Gunnar Wortmann told The Associated Press that there were "three explosions near the (Borussia Dortmund) team bus as they left the hotel to go to the stadium" and that "there was one player injured inside and damage to a window."
Police say the explosions took place in the run-up to the match at around 7 PM local time.
Dortmund is in western Germany, in the densely populated Ruhr industrial region.
Inside the packed stadium, supporters of Monaco, which plays in the French league, chanted "Dortmund, Dortmund" in sympathy for the German side.
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