The steps are the only way to reach Selwicks Bay, meaning the beach is also temporarily closed.
There are also concerns paddle boarders arriving at the beach from nearby North Beach may find themselves stranded, or have to turn back, as they no longer have a way up the cliff.
The council said engineers and contractors were working on a solution, but the steps were likely to be closed for some time.
Nick Coultish, the council’s cabinet member for culture, leisure, tourism and planning, said: “We don’t want to restrict access to this beach but these steps are in a dangerous condition, so we had no choice but to close them.
“Please don’t ignore the barrier and closure signs, because there is a real risk that someone could get seriously hurt if the steps give way.
“This won’t be a quick repair, unfortunately. The damage means we may have to rebuild them.
“We look forward to reopening these steps when they are made safe, but until then please don’t use them.”
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