Anne, an Olympic-medal winning horsewoman, was walking on her Gloucestershire estate on Sunday evening when the incident happened.
Emergency services were dispatched to the estate and, after medical care at the scene, the princess was taken to Southmead Hospital in Bristol for tests, treatment and observation.
"The Princess Royal has sustained minor injuries and concussion following an incident on the Gatcombe Park estate yesterday evening," Buckingham Palace said on Monday
"Her royal highness remains in Southmead Hospital, Bristol, as a precautionary measure for observation and is expected to make a full and swift recovery.
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"The King has been kept closely informed and joins the whole royal family in sending his fondest love and well-wishes to the princess for a speedy recovery."
The exact cause of the injuries is unconfirmed but Anne's medical team said her head injuries were consistent with a potential impact from a horse's head or legs.
It is understood the 73-year-old princess was walking within the protected perimeter of Gatcombe Park estate when an incident occurred.
Her husband, Vice Admiral Tim Laurence, who was on the estate at the time, accompanied her to hospital.
"Her royal highness is recovering well, is in a comfortable condition and is being kept in hospital as a precautionary measure for further observation," a Buckingham Palace spokesperson said
Anne's daughter Zara Tindall and son Peter Phillips were also on the estate at the time, but it is not known who raised the alarm.
Anne will miss several engagements this week, including the state banquet for the Japanese state visit on Tuesday and a visit to Canada.
The Princess Royal is one of the hardest-working members of the royal family, having stepped in and taken more duties in light of Charles' cancer diagnosis.
Reuters, AP and PA
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