Dortmund defender Marc Bartra was injured in the incident and is currently in hospital, where he will undergo surgery on a fractured arm.
The game will be played at 5:45pm UK time on Wednesday April 12.
Local police confirmed that there were three explosions in the area surrounding the team bus. After an initial investigation they later clarified that they were "working on the assumption" the attack had been carried out with "serious explosives". The bus was damaged in two places near the back right tire.
Police have confirmed they are looking for a car with a foreign registration plate in connection with the incident and revealed that they discovered a letter near the scene of the crime.
Dortmund said in a statement on the club Twitter account: “Bomb explosion by the team bus at the team hotel.
“Players are safe. No danger in and around the stadium.”
Supporters who had already arrived at the game were advised to remain in the stadium. Monaco fans were recorded chanting "Dortmund" in a show of solidarity with their hosts.
European football's governing body Uefa said: "This decision was made after a meeting held at the Westfalenstadion between UEFA, representatives of the two clubs and local authorities."
Police Dortmund said in a statement: "In the run-up to the Champions League game between BVB (Dortmund) and AS Monaco, there was just after 1900 tonight an explosion close to the BVB team bus."
"According to what we currently know, the wheels of the bus (totally or partly) burst and one person was injured.
👍 Thank you for your support in and outside the stadium and your kind messages throughout the whole world. #bvbasm— Borussia Dortmund (@BVB) April 11, 2017
"It is not yet possible to say exactly what the explosion was or exactly where something exploded."
They later added: To reassure stadium visitors and relatives: There are currently no indications of a threat to visitors in the stadium."
Spanish prime minister Mariano Rajoy tweeted that he was "following the information that is coming from Dortmund" and wished a "speedy recovery" to Bartra.
Bartra's former club Barcelona also wished him well in his recovery.