Gary Baker, who was walking nearby, said the branch came "crashing down" from a 60ft (18.2m) tree along a footpath that leads to a restaurant in the botanic gardens, in South-West London.
"There was a bang and I jumped around at what sounded like three or four gunshots," he said. I looked and could see what remained of the branch.
"I didn't see it hit the woman but it was quite clear she was badly hurt. Someone shouted, 'call an ambulance' as she lay face down on the ground.
"The branch was extremely large. It was 12 inches (30.5cm) thick at least. It was near her but not on top of her.
"I helped another man to turn her over, on the instructions of the 999 operator, to give her heart massage ... Paramedics arrived but they could not save her."
Mr Baker, a telecoms manager, said: "I heard someone else saying it was like a bolt of lightning. But I didn't see any, it was not that sort of weather.
"There appeared to be at least another couple who were with her, dressed in similar clothes, but they did not say very much. It was a massive shock."
A spokesman for the Royal Botanic Gardens at Kew said: 'We can confirm a tragic accident at Kew Gardens this afternoon when a falling tree branch resulted in a fatality.
"We are currently working with police and next of kin are being informed.
"We cannot comment further at this stage but our deepest sympathy is with family and friends."
A Metropolitan Police spokesman confirmed officers were called to the scene and said the matter may be referred to the Health and Safety Executive.
- Daily Mail additional reporting nzherald.co.nz
