The German team confirmed one of its players has been injured following the explosions 10km from the Signal Iduna Park stadium in Dortmund, North-Rhine Westphalia in east Germany.
The player is believed to be Spanish defender and father-of-one Marc Bartra, who has been taken to hospital.
He is thought to have suffered cuts to his hands from shattered glass after the bus’ windows smashed.
The quarter-final against Monaco has been postponed until tomorrow at 6.45pm after the German team put a message on the stadium screens informing fans of the incident.
Borussia Dortmund (BVB) has told fans to stay calm as emergency investigators attend the scene.
In a tweet, the club said: “We will inform you as soon as there is news.”
The explosions are said to have come from a bush in Wittbräuckerstraße, 10km from the stadium where they were due to kick-off at 7.45pm local time (6.45pm GMT).
Monaco fans have started singing “Dortmund, Dortmund” in response to the incident, with the tunes being “very warmly received” by Dortmund fans.
A statement form Dortmund Police, said: “In the run-up to the Champions League match of the BVB against the AS Monaco, there was an explosion near the BVB team teambus shortly after 7 pm.
“The event location is Wittbrauckerstrasse / Schirrmannweg in Dortmund-Hochsten.
“According to current knowledge the disks of the bus (whole or partial) were broken and one person was injured.
“It is not yet possible to say exactly what the explosion was or exactly where something exploded.”