It is the latest attack in the drought-stricken Laikipia region by suspected herders, who have been invading private property in search of fresh grazing.

There were no visitors staying at the Mukutan Retreat at the time of the attack, according to local reports.

The attack may have been retaliation for a police operation, reports said.

Earlier this week, police reportedly shot dead about 100 cattle in the surrounding Laikipia Nature Conservancy, which is owned by Ms Gallmann.

Ms Gallmann, who is best known internationally for her memoir I Dreamed of Africa, has not commented.

Her daughter, Sveva Gallmann, also a conservationist, described being caught up in the attack:

"Our operations buildings and our house came under direct gunfire from armed men," Reuters news agency quoted her as saying in a statement.

"My nine-month-old daughter was in the house with her carers and I was shot at three times as I ran between the buildings to get to her."

Laikipia, which covers about 10,000 sq km in Kenya's central highlands, is where some of the country's largest white landowners are based.

Insecurity has risen sharply in recent months as a drought has led armed herders to seek out new pasture, pitting them against big landowners and smallholders.

Tens of thousands of cattle are thought to have been driven onto private land and at least a dozen people have been killed.

British rancher Tristan Voorspuy, who also ran a safari company, was shot dead in early March while inspecting his lodges in Laikipia.

Hundreds of herders have been detained as part of police operations, and the authorities have accused some local politicians of using racially charged language and inciting locals to occupy private property illegally, ahead of general elections due in August.

The MP for Laikipia North, Matthew Lempurkel, was charged with incitement earlier this month.

An additional factor, some of the landowners say, is that there is now just too much livestock in the region, causing overgrazing and destruction of previously fertile land.

The BBC's Ferdinand Omondi in Nairobi says the pastoralists appear now to have resorted to a scorched earth policy in their battle for grazing.

As well as the attack on Ms Gallmann's lodge, they set about 4 sq km of the Laikipia Nature Conservancy on fire.

The herders accused police of trying to force them off the land by shooting their livestock. Police say the livestock were killed in crossfire with the herders, who were using the animals as shields.

The BBC's Alastair Leithead tried to approach herders last month to ask about their grievances, but was forced to retreat when they shot at him.

Ms Gallmann owns about 360 sq km in Laikipia, which is home to rare wildlife, birds and trees. Her organisation also runs community, education, arts and sports projects.

The Mukutan Retreat lodge is made up of four stone and wood cottages, perched on the edge of the Mukutan Gorge.

Visitors can pay more than $650 (£525) a night to stay there, according to travel websites.