The Shrewsbury to Newtown stretch of the Cambrian line will be closed for the foreseeable future as a result of the damage, with a bus replacement service set to operate between the towns.
The damage has been caused to a stretch of the line just outside Welshpool on the way to Newtown, where large parts of the earth supporting the track have been washed away.
Engineers have been on site near Welshpool since Tuesday, using drones and specialist equipment to assess the scale of the damage.
In at least 12 locations along half a mile, ballast – the stones supporting the track – has been completely washed away by the force of the floodwater caused by Storm Franklin.
A spokesman for Network Rail said the full extent of the damage will be established over the next few days, as further investigations take place.
Network Rail Wales & Borders route director, Bill Kelly said major repair work would be needed to make the route safe.
He said: “I’m very sorry for the disruption to our passengers on the Cambrian Line. Fast flowing flood water of biblical proportions has devastated a section of the railway south of Welshpool, and it’s going to require extensive repairs before we can safely reopen the line.
“The images from site speak for themselves, there are multiple sites where the ballast supporting the track has been completely washed away. With climate change, we’re seeing more and more extreme weather like this so it’s vital we continue our mission to build a more resilient railway for Wales and Borders.”
Jan Chaudhry-Van der Velde, managing director of Transport for Wales, added: “We understand closures are incredibly frustrating for passengers and we will be supporting colleagues in Network Rail to ensure the line reopens as soon as possible.
“We’re still dealing with significant flooding in the area, but we are now able to operate replacement road transport to Newtown, where rail services to Machynlleth will now start. Passengers are advised to check the Transport for Wales website, app or social media channels for the latest information before travelling.”
The county's rail network also faces disruption between Shrewsbury and Hereford.
Storm Franklin caused a land slip next to the line in Craven Arms, closing the route, with repair work required which is expected to be completed in the coming days.
A spokesman for Network Rail said: "Storm Franklin also led to extensive damage between Shrewsbury and Hereford. Engineers have been working to repair the damage as quickly as possible and we expect this line to reopen in the coming days."