The cliff collapsed onto the shore at Barton-on-Sea on Tuesday evening.
New Forest District Council said an assessment by its coastal scientists had revealed further movement and another landslip "is highly likely".
While no-one was injured by the collapse, visitors are being asked to avoid the area of the cliff top and the beach below.
The area is expected to remain closed until the cliff stabilises.
A cliff top and section of beach in Hampshire have been shut following a landslip.