The front bumper of one bus was ripped off, following the crash at the junction of Stamford Road and Birmingham Road, just after 1pm yesterday.
However it is not believed anyone was injured in the incident.
National Express has since apologised to its customers and confirmed a full investigation has been launched.
National Express spokesman Ali Bell said: "There was an incident on Tuesday at just after 1pm involving two National Express West Midlands buses and a van.
"It happened at the junction of Stamford Road and Birmingham Road in Stourbridge.
"There was minor damage to all three vehicles.
One single-decker bus saw its front bumper taken off and windscreen cracked, while the side of another bus, a double-decker, had its metal chassis ripped down the side.
"National Express West Midlands is carrying out a full investigation into what happened.
"We'd like to apologise to anyone whose journey was delayed by this incident."