The buses, run by Avondale, crashed in Drumchapel at around 7.30am.
Emergency services were called to the scene after the vehicles crashed into each other in Kinfauns Drive.
Both drivers and one passenger, the only one on board at the time, were taken to the city's Western Infirmary. Both drivers escaped with minor injuries while the passenger is thought to be suffering from neck injuries.
Rain and sleet turned to ice overnight as freezing temperatures led to black ice on the city's roads.
An eyewitness said the road resembled an "ice rink".
A police spokeswoman said they were probing the cause of the crash.
Police closed the road between Linkwood Drive and Kinclaven Avenue in the wake of the incident and diversions are in place.
David Gold of Avondale Coaches claimed icy road conditions and a lack of grit were to blame for the accident.
Mr Gold added: "Kinfauns Drive is a bus route so we would have expected it to be attended to. The road was sheet ice and at that time of the morning it was dark.
"Luckily the driver was going slowly at the time. We're glad everyone is going to be OK."
Meanwhile, four vehicles were involved in a road crash in Fountainwell Road in the city's Sighthill shortly before 9am today.
One person was injured.