The incident took place at junction 10 on the M65 motorway following the game at Turf Moor on Sunday afternoon, police said.
Burnley Football Club said they were "saddened and dismayed" to learn about the attack.
"Having spoken with Villa we are relieved to hear nobody was hurt in the incident," the club added.
"We strongly condemn this behaviour and will support Lancashire Police in their efforts to find whoever was responsible."
Lancashire Police said a brick was thrown at the bus which struck the windscreen and caused some damage to the vehicle.
Supt Melita Worswick said: "It is nothing but good fortune that the brick didn't cause more damage, or result in somebody being seriously injured or even killed.
"We cannot say at this point whether this was a targeted attack but enquiries are ongoing and this will form part of our investigation."
The result marks Burnley's second defeat since their return to the top flight.
Aston Villa declined to comment on the attack on their bus.