Police were called to the bus stop outside Pet & Aquatic World in Armley Road at 2.25pm.
Staff from the ambulance and fire service also attended the scene.
The driver, a 54-year-old man, had been sprayed in the face by a passenger who had tried to get off before the stop and then forced the doors open to leave on the First West Yorkshire service.
The culprit used a CS type spray or something similar, it is thought, but was not harmful.
A 20-year-old woman passenger was also taken to hospital after having an asthma attack. She was treated and released a short time later.
Inspector Sarah Towers, who heads neighbourhood policing for west Leeds, said: “This was a very distressing incident for the driver and the passenger affected by this substance and also for the other passengers who were on the bus.
“We are carrying out extensive enquiries, including checks on CCTV from the bus and in the general area, and would like to hear from anyone who witnessed the incident or saw the suspect leaving the scene.
“Thankfully the substance used doesn’t appear to have caused any lasting effects but we are treating this incident seriously.
"Clearly someone who is prepared to illegally carry and use something like that in an unprovoked attack needs to be caught as soon as possible.”
The driver experienced stinging to his eyes, nose and throat and was treated at the scene before being taken to hospital to be checked over.
Tests by the fire service confirmed that the substance used was not harmful. It is believed to have been a CS type spray or similar.
The suspect, who was described as white, about 5ft 11ins tall and of average build, had got on the city-bound number 72 First service at Armley Ridge Road.
He walked off in the direction of Branch Road after the attack.
Will Pearson, Operations Director at First Leeds: “We can confirm that our driver has attended hospital as a precaution and we’d like to thank customers for their messages of concern for his wellbeing.
“We are now working with the Police and assisting them with their investigation into the matter. We would urge anyone with information to contact the Police immediately.”
Anyone with any information that could assist the investigation is asked to contact officers via 101 quoting crime number 13180156078 or call the independent charity Crimestoppers anonymously on 0800 555 111.