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.

Openers Mark Stoneman (93) and Phil Mustard (88) shared a 180-run first-wicket stand and Scott Borthwick hit a quickfire 63 off 53 balls as the Jets pummelled 340-6 from their 50 overs.
A century stand between Kevin O'Brien (89) and Mark Cosgrove (63) put the Foxes on course for their target.
They were restricted to 329-9, though, as paceman Jamie Harrison claimed 4-40.
Earlier, Mustard looked to attack for Durham from the first ball and hit 10 fours and four sixes before being caught off Kevin O'Brien after facing just 70 balls.
Stoneman and Borthwick later fell in quick succession to Rob Taylor (4-58) as Leicestershire tried to stem the scoring rate.
Their response began disastrously as Chris Rushworth bowled Mark Pettini and Harrison had Neil Dexter caught behind to reduce them to 26-2.
O'Brien and Cosgrove shared a 115-run third-wicket partnership to put Leicestershire back in the match, but the former was caught off Harrison as Durham held on to win.
Leicestershire all-rounder Kevin O'Brien told BBC Radio Leicester:
"To get close when chasing a big total is disappointing but we probably have to blame ourselves.
"Three of us who got in, myself, Cossie and Niall (O'Brien), if we're being honest, we threw our wickets away at crucial times.
"If one of us had gone on and got 100, 110, 130, we'd have been on the other end of this result."
Durham batsman Phil Mustard told BBC Newcastle:
"The pitch today was a little bit better, we had the odd one that did a little bit but as the day went on, it did get better.
"Once your two openers get you off to the start that we did today, I think 330, 340 was always going to be our target.
"Scotty came in at number three and did a fantastic job, and then the boys near the end of the innings put on a nice partnership, and the bowling was really good as well."
A cliff top and section of beach in Hampshire have been shut following a landslip.
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Durham earned a narrow 11-run victory over Leicestershire in a high-scoring One-Day Cup match at Grace Road.