The car hit the bridge on the A5191 Belle View Road in the early hours of this morning, leaving a substantial hole in the wall.
It has resulted in the railway line being closed between Shrewsbury and Welshpool and led to delays for drivers on Belle View Road and Hereford Road.
Police said part of the bridge was knocked onto the railway tracks below.
A5191 Belle Vue Road. An RTC has resulted in part of the bridge being knocked onto the railway below. Expect road and rail (Welshpool/Aberystwyth line) disruption to continue into the morning, at least. @OPUShropshire @WestMerciaOCC pic.twitter.com/DLhS6qRexn— Oscar Mike 28 (@OscarMike28) March 15, 2019
It is not yet known how long disruption will last but it is likely to continue until at least 3pm, Transport for Wales said.
Services between Birmingham, Shrewsbury and Aberystwyth are affected.
The bridge is only partially shut so drivers are still able to pass, but there is congestion nearby during rush hour as a result.
Rail replacement buses are being put on by Lakeside Coaches between Shrewsbury and Welshpool, but these were also facing delays after a crash shut the main road between the two towns for around an hour.
⚠️ Due to a road vehicle colliding with a bridge between Welshpool and Shrewsbury the line is closed— Trafnidiaeth Cymru Trenau Transport for Wales Rail (@tfwrail) March 15, 2019
Disruption is now expected until 15:00 15/03.
⚠️ Oherwydd bod cerbyd wedi taro a phont rhwng Y Trallwng ac Amwythig, mae'r llinell ar gau
Rhagdybir afloynyddwch tan 15:00 15/03 pic.twitter.com/ppbktq7vxX