Merseyside Police in Liverpool are investigating the pre-game incident which occurred when the visitors were arriving at Liverpool’s Anfield stadium.
The police say approximately 400 people were on site and that a “number of items were thrown” at the vehicle, while pyrotechnics were also lit in the area.
Images from the scene show an outer pane of a double-paned glass window smashed out but police confirmed there were no injuries.
“We condemn unequivocally the actions that led to Real Madrid’s team bus being damaged during its arrival to Anfield,” said a Liverpool spokesperson in a statement to CNN Sport.
“It is totally unacceptable and shameful behavior of a few individuals. We sincerely apologize to our visitors for any distress caused.
“We will work together with Merseyside Police to establish the facts and identify those responsible.”
Authorities say they are now looking through CCTV footage of the incident and working closely with Liverpool to establish who was involved. They urged anyone with social media footage to get in touch.
“As with all matches, we have worked very closely with both clubs to ensure the safety of the public and the teams themselves, and the disgraceful behavior of those involved this evening is extremely disappointing and totally unacceptable,” Merseyside Police Chief Superintendent Zoe Thornton said in a statement.
“Such incidents will not be tolerated under any circumstances.”
Real Madrid was not immediately available for CNN Sport’s request for comment.
The game itself ended in a goalless draw, meaning Real progressed into the semifinal of the Champion League after its 3-1 victory in the first leg. Madrid will meet Chelsea in the last four as it bids to win a record-extending 14th European Cup.
Elsewhere in the Champions League, Manchester City reached the semifinal after defeating Borussia Dortmund 4-2 on aggregate. It will now face Paris Saint-Germain for a place in the final.
CNN’s David Close and Homero De la Fuente contributed reporting.