The incident happened at the James Callaghan Drive junction on Portsdown Hill Road shortly after 1pm.
The bus was carrying five people on board at the time of the accident.
Two people sustained minor injuries, one of which was an ankle injury.
No other vehicles were involved.
The bus was operating a park and ride service for staff working at Queen Alexandra (QA) hospital in Portsmouth.
The road was closed while the vehicle was recovered and was cleared by 3.40pm.
A spokesperson for South Central Ambulance service said: "We received a 999 call at 13.19 with the caller reporting that a single decker bus had come off the road and hit a tree on James Callaghan Drive, Portsmouth.