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.

Webber, who arrived from Huddersfield in April, is heading up the search for a permanent replacement for Alex Neil.
"We have a list of candidates, and once their seasons are finished, we can start to accelerate that process," Webber told BBC Radio Norfolk.
Northern Ireland boss Michael O'Neill has distanced himself from the role.
Neil was sacked by the Canaries on 10 March, with Alan Irvine taking the team on an interim basis for the rest of the season.
Webber said he still expected the new head coach to be in place by the end of May.
"We have a clear idea of the type of person it'll be," he added.
"Things are a little bit slow because people's seasons are still going on and we have to be respectful of that.
"There's certain rules that we have to adhere by."
Webber also reaffirmed Norwich's interest in signing Ajax left-back Mitchell Dijks, 24, on a permanent deal, following a successful loan spell, while playing down speculation over Steven Naismith's future at Carrow Road.
"With Mitchell, we have the option to buy him, so to a certain degree it's our call," he said.
"We need to agree personal terms and from a financial point of view we need to be creative with the squad, so if that means Mitchell or any other player we're trying to get falls out of that, we can't do it.
"I had a laugh with Steven the other day about what came out of the media in Scotland, saying he was going to be let go on a free.
"It's news to me, and it's news to Steven. He's a good player, we all know that, [with] unbelievable experience at the highest level, in terms of international football.
"He's our player, he's under contract."

Gadlys Rovers' players found the goalposts facing away from pitch just hours before kick-off at Abernant in Rhondda Cynon Taff.
It would have been impossible to score a goal as the stanchions that holds the net were pointing into the pitch.
The amateur team play in the Aberdare Valley Football League.
"I was amazed when I went to check the pitch," said team manager Matthew Jones.
"To the right hand side I could see there was something wrong with the goals. They were the wrong way round.
"I thought to myself: 'What the hell is going on?'"
The 24-year-old boss was live streaming his pitch inspection in Abernant to his players when he made the discovery.
Mr Jones complained to Rhondda Cynon Taf council and he said they maintained council workers had installed the goalposts correctly.
"There's no way we could've played if it hadn't been sorted out," he added.
"When I came back around 5.15pm they had been turned around the right way."
A council spokesman said it had investigated the incident but later declined to comment further.
Kenya's Wildlife Service says it is pursuing a gang of poachers they suspect of killing an entire family of 11 elephants.
[NEXT_CONCEPT]
Norwich City's next head coach will come from a shortlist of managers currently in jobs, sporting director Stuart Webber has said.
[NEXT_CONCEPT]
A football team has found a novel way of keeping a clean sheet - as the goalposts on their council-run pitch were installed the wrong way round.