The 40-year-old, who is based near Malpas in Cheshire, fell from her mount Topwood Beau and was airlifted to Bristol's Southmead Hospital.
British Eventing (BE) said she suffered a traumatic brain injury in the fall on 6 May.
In a further update on Monday, BE said she is now recovering at home.
She spent more than a week in intensive care following the accident.
"Thank you so much to everyone for their kind thoughts, messages and support since my fall at Badminton Horse Trials," she said in a statement.
"It is just four weeks since Badminton and I am now recovering at home after an intense programme last week at the Injured Jockey's Oaksey House in Lambourn.
"I owe a huge debt of thanks to everyone involved in the Medical Support at Badminton, the Intensive Care Unit at Bristol's Southmead Hospital, the Royal Stoke University Hospital and the team at Oaksey House, without whom I would not be so well on the road to recovery. Thank you all."
Topwood Beau, a 14-year-old gelding, was uninjured in the fall, which happened at the third fence - Keepers Question - on the cross-country course.
Gilruth, who is married with two young daughters, made her Badminton debut in last year's event.
She has competed in British Eventing competitions for 18 years and runs her own yard.
British rider Emily Gilruth has left hospital after she was seriously injured in a fall at the Badminton Horse Trials.