Three explosions damaged the vehicle as the squad were making their way to the Westphalenstadion ahead of kick-off in the first leg of their quarter-final match, which will be replayed tomorrow.
Spanish defender Marc Bartra was taken to hospital, where he is to undergo surgery to repair a fracture in his arm and remove shrapnel.
Watzke said in a statement: "An explosive strike on the bus was carried out immediately after the departure from the hotel.
"Three explosive devices were placed and triggered on the edge of the road.
"The whole team is in shock. We have to get through this. It will not be easy for the players. I hope that the team will somehow be able to return to the field.
"Borussia Dortmund is especially strong in extreme situations. Everyone will come even closer together and I'm sure the team will feel this."
Club president, Reinhard Rauball, added: “Of course this is an extremely difficult situation for the players. But they are professionals, and I am convinced that they will put it aside and perform.
“It would be a bad thing for those who did this to succeed in influencing the team in some way.”
At 19:45pm UK time Dortmund and Uefa announced that the game would be rescheduled for Wednesday, when the game will kick-off at 17:45pm.
Watzke added of the timing of the rearranged match: "We decided that the match was cancelled and that we would return on Wednesday at 1845 (CET), so we did not clash with the Bayern Munich-Real Madrid game (2045 CET kick-off) and give the opponents from Monaco the opportunity to leave early in the evening."
Dortmund goalkeeper Roman Burki gave Blick his account of what happened. “The bus turned on the main road when there was suddenly a huge bang, a proper explosion.
“The police were quickly on the spot and handled the situation. We were all in shock … After the bang we all ducked and those who could lie on the floor did so. We didn’t know what was going to happen next.”
Supporters from both sides were kept in the stadium for some time before being moved out, with Monaco supporters chanting “Dortmund! Dortmund!” in support of their hosts.
Meanwhile local residents in Dortmund have been offering Monaco supporters a place to stay as they wait for the rearranged fixture, using the hashtag #bedforawayfans.
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.