The Diana, Princess of Wales, Memorial Fountain in Hyde Park will remain closed for the weekend after three visitors slipped and hurt themselves.
The fountain was opened two weeks ago
Two adults and a child were taken to hospital on Thursday after falling in the same place on the east side of the source pool, the Royal Parks said.
An investigation has been launched and designers are considering ways to make it safer.
The £3.6m memorial was opened by the Queen two weeks ago.
Theo Moore, a spokesman for the Royal Parks, said engineers and designers were meeting to discuss solutions.
"We are concerned and we are going to get to the bottom of the issue as soon as possible," he said.
The monument has been surrounded by a 7ft high barrier to enable a detailed investigation to be carried out.
Meanwhile laminated signs have been placed around the area of the memorial, encouraging visitors to enter the surroundings of the fountain.
The two adults and the child, who suffered a "bump to the head" and "some bleeding", have been discharged from hospital.
Last week the water was stopped due to a blocked pump while the previous week it was blocked by fallen leaves.