Barbara Gale described the incident to Radio Sport
"He had actually completed the course, jumped the last fence, when the horse apparently stumbled, and there was a crashing fall of both horse and rider," she said.
"One of my listeners said to me that there was this dreadful thump as they hit the ground."
Gale said both got up, but after that Nicholson felt extremely unwell.
"I can only say that knowing Andrew very well over the years, that it can't just be a little knock to keep someone like Andrew Nicholson in hospital."
"Over here and especially here in Wiltshire, he's a star to us."
Nicholson was in the lead when his horse fell.
Gale said she rang his home after the event, and was shocked to be told by the family's nanny that he'd deteriorated.
"She said that they honestly did not know at the time what the matter was, whether it was a head injury or a broken bone."
Another competitor who saw it said it was very worrying.
Nicholson has won three Olympic medals (silver in 1992, bronze in 1996 and bronze in 2012) in six appearances. Nicholson and equestrian teammate Mark Todd were the first New Zealanders to compete in six Olympics.
Nicholson has won the Burghley horse trials five times.