The three slipped on stone steps that are part of the granite structure in Hyde Park, said Royal Parks spokesman Theo Moore. One was a child who suffered a bump on the head and some bleeding. The two others were adults, but the Royal Parks did not know how seriously they were hurt.
"We are obviously very concerned about their welfare and hope they recover swiftly," Moore said. "We immediately switched off the flow of water and will not be turning it back on until we are satisfied it is safe to do so. A full and thorough investigation has already started."
Moore said the water was turned off at 3 p.m. and would not be turned on until the investigation is finished and any needed safety measures are added.
Queen Elizabeth II officially opened the fountain this month at a ceremony attended by Diana's ex-husband Prince Charles, sons William and Harry and brother Earl Spencer.
The fountain ran into trouble a day later, overflowing during a fierce storm. Leaves blocked the fountain's outflow in high winds, and the Royal Parks had to assign extra staff to keep it clear of debris.
The fountain is an oval, roughly 260 feet by 165 feet. Water flows from the highest point down both sides into a basin called the Tranquil Pool.