Police have charged four teenage boys in connection with the incident, which happened while the service was travelling along Gorbals Street at around 2.40pm.
The victims were taken to Queen Elizabeth University Hospital for treatment.
A police spokesman said: “We can confirm four male youths – aged 16, 14, 14 and 13 – have been charged in connection with a disturbance on Gorbals Street on Sunday, 4 October.
“Inquiries are ongoing.”
Duncan Cameron, First Glasgow operations director, said: “I can confirm that a serious assault to two teenagers occurred on board one of our Sunday afternoon services.
“We are doing all we can to assist Police Scotland with their investigation into the incident including making the CCTV footage available.
"I would like to praise the driver for his quick reactions to aid the injured passengers.”