The family was gunned down on Saturday in the single worst incident of ivory poaching recorded in the country.
Kenya has recently taken a more aggressive stance against poaching as it tries to combat a surge in demand for ivory from Asia.
About 100 elephants are killed each year in Kenya by poachers.
Despite a long-standing ban on the international trade, ivory from elephants is often smuggled to Asia for use in ornaments, while rhino horns are used in traditional medicine.
Saturday’s killings took place in Tsavo National Park, Kenya’s largest single continuous ecosystem, which is home to some 13,000 elephants.
“[It] shows the great lengths these criminal cartels are ready to go to get ivory. It’s really tragic,” Kenya Wildlife Service spokesman Paul Udo told Reuters news agency.
He said the poaching gang is believed to be made up of 10 people and was being hunted by rangers on foot and from the air.
In a statement, the Wildlife Service said that all the elephant carcasses had bullet wounds.
The Kenyan government banned trade in ivory in 1989, and levels of elephant poaching subsequently declined, but there has been a rise in the illegal practice in recent years.