Ms Gallmann, the author of I Dreamed of Africa, is said to be in a stable condition having undergone a seven-hour operation in a Nairobi hospital.
Joseph Nkaissery, Kenya's interior minister, confirmed that the suspects were killed by security forces and added that a gun was recovered and several other arrests have been made in relation to the attack.
While Mr Nkaissery described the attack as “isolated banditry activity”, the Laikipia region where it occurred has seen a wave of violence in recent times as herders have been invading private property in the drought-stricken area in search of fresh grazing land.
The drought, which has affected half of Kenya and been declared a national disaster, has seen more than 30 people die at the hands of conflict over grazing land.
Ms Gallmann owns around 360 square kilometres in Laikipia, and as well as the Laikipia Nature Conservancy, she also ran a luxury safari lodge which was burnt down last month.
Born in Italy, Ms Gallmann moved to Kenya in 1972 with her husband and son, who both died in separate incidents years later.
She is now a Kenyan citizen and her novel, I Dreamed of Africa, was turned into a biographical drama film starring Kim Basinger.
