Efforts are currently underway to resolve the problem, though no specific timeline for reopening has been provided.
In the meantime, commuters and pedestrians are advised to seek alternative routes.
The Uber Boat by Thames Clipper is available from Woolwich Pier, with ferry services running until 10pm daily.
A spokesperson for the Royal Borough of Greenwich Council said: “Woolwich foot tunnel is closed until further notice because of a public safety issue.
“We are working to rectify this as soon as we can.
“Please use an alternative route.
“The Uber Boat by Thames Clipper can be boarded at Woolwich Pier and the ferry runs until 10pm.”