He was later seen running on Prestonpans High Street, external, about 2.5 miles (4km) away, still wearing his race saddle and number seven banner.
Ground staff were able to track the horse down before returning it to the stables in the horse ambulance.
Trainer Gary Rutherford told BBC Scotland Rufio was “home safe and well” following the incident, adding that jockey Ms Brown was also unharmed.
A Musselburgh Racecourse spokesperson said: “A horse unseated its rider in the last race and made its way out of the racecourse.
“This is an extremely rare occurrence and happily the horse was returned unscathed to the racecourse by our ground staff after its short journey towards Prestonpans.”
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