The Follow the Dog and Monkey mountain biking trails were damaged in the wake of Storm Ciara and closed on Monday while the fallen trees and debris are cleared.
Forestry England hopes the routes will be reopened within days, but is also waiting to see how Storm Dennis affects the trails this weekend.
A spokesman for Forestry England said: “Unfortunately our Follow the Dog and Monkey mountain biking trails have been damaged in the wake of Storm Ciara and are temporarily closed whilst we clear the fallen trees and debris.
"We’ll get the trails open again as soon as possible. In the meantime our green and blue cycle routes are open as normal.”
The West Midlands will be struck by another burst of heavy rain and gales from Storm Dennis over the weekend.
WATCH the latest Met Office forecast
The fourth named storm of the 2019-20 season, Dennis, is set to bring a second consecutive weekend of wet and windy weather after Ciara struck the UK with winds of up to 97mph.
Gusts of 50mph are expected, with more than 60mph possible over hills, coastal areas and exposed locations, the Met Office said.
Predicted heavy rain could also run the risk of further flooding, with 43 warnings still in place in England, six in Scotland and one in Wales following recent heavy rainfall.