Conservationist Kuki Gallmann is in the Intensive Care Unit, the family has said.
Gallmann was airlifted to Aga Khan hospital on Sunday after she was shot in the stomach by armed raiders at her conservancy in Laikipia.
The family said Gallmann was shot and wounded by an organised gang of gunmen at around
9am on the Laikipia Nature Conservancy
Her vehicle was ambushed and she received a gunshot wound to the stomach.
After the assault, Gallmann
was airlifted to Nanyuki where she was treated by British army medics and then flown by helicopter to Aga Khan Nairobi.
She entered surgery at 1pm and underwent a 7-hour operation.
The family thanked Kenyans for the huge support they have offered.
"From friends, family, and well-wishers for which we are extremely grateful," they said.
They also thanked the Kenya Wildlife Service, Tropic Air, the British army, Aga Khan Hospital and our team of doctors for their support and swift intervention," they said.
Earlier, Interior CS Joseph Nkaissery said several people have been arrested in connection with shooting of Laikipia rancher.
He said police have recovered a gun suspected to have been used to shoot her.
Nkaissery said the gun is undergoing ballistic tests to confirm whether it was the one used in the shooting in the "isolated incident of banditry".
He said the operation to flush out bandits who have invaded private ranches in Laikipia and Baringo is going on well.
On Sunday,Interior Ministry spokesperson
said investigations are ongoing and the perpetrators of the crime will soon be arrested.
“The Government wishes to re-assure residents of Laikipia and Baringo Counties as well as residents in all other parts of the country that the we will do everything possible to ensure that law and order are preserved at all times despite efforts by criminal elements to undermine security,” Mwenda said.
Laikipia farmer's association (LFA) condemned the attack and called for the swift disarmament of militia causing havoc in the larger Laikipia region.