The injuries are consistent with impact from a horse's head or legs, a source said.
The royal pair will also reportedly spend less time in Australia than originally planned.
The picture comes just hours after Kate made her return to public life.
She joined other British royals on the balcony of Buckingham Palace for the King's official birthday.
A source also claims she could soon be releasing a new video.
Almost two years after her death, new pictures of Queen Elizabeth II have emerged for a new Buckingham Palace exhibition.
The couple are on their first trip to Africa's most populous nation, prompted by links forged through the Invictus Games.
"I hope they will be back. It's really personal."
The picture was taken a few days ago.
