The university spokesman said there was no one on the bus other than the driver and that no one was in the parked cars.
The crash happened on Whitney Avenue and Linden Street just after 7:45 a.m.. Two lanes had been closed due to the accident.
New Haven Police are investigating the cause of the crash. The driver, a 51-year-old man from New Haven, appeared to be uninjured but was taken to the hospital to be checked out.
The driver told police he was at the end of his shift when he veered into the line of parked vehicles. Driver fatigue is the likely contributing factor, according to police. He was issued an infraction for failing to drive in a proper lane.