The London Olympian, from Northallerton, had three horses in the frame for selection and was part of a 10-man shortlist announced last month.
However, the GB selectors omitted the 39-year-old when a team of four riders and a reserve was announced on Tuesday
Former world No. 1 William Fox-Pitt leads the team on 16-year-old stallion Chilli Morning. Gemma Tattersall has two potential runners in Chico Bella P and Quicklook V*, while Kitty King and Ceylo L A N and Izzy Taylor and Allercombe Ellie also got the nod.
Grand slam winner Pippa Funnell will act as the team’s reserve with her horse Billy the Biz.
Wilson, who was part of the Team GB team that won a silver medal at London 2012, said: “It was inevitable there was always going to be some disappointed riders and owners.
I have been nominated the home 1st reserve with ‘One Two Many’ and although we have dreamt of Rio and driven and worked for the dream, it is to be ‘so close yet so far’
“I am genuinely delighted for the riders, their support team and owners who have been selected.
“We are a close community and I am sure the decision was a difficult one, but now we get behind those chosen and support and cheer them all the way.”