The agency added that additional security measures had been taken to prevent any further attacks.
Nairobi National Park lies just 10km (six miles) from the city centre and is home to animals such as lions, buffalos, giraffes, leopards and cheetahs.
It is fenced on three sides to stop animals roaming into the city but it is open to the south to allow animals to migrate in and out of the area.
While lions often come into conflict with humans in Kenya, especially over livestock, it is not common for people to be killed.
Last year, CCTV footage captured the moment a lion snatched a Rottweiler dog from another home near Nairobi National Park.
KWS also reported that a 54-year-old man was killed by an elephant on Saturday.
The incident happened in the central Nyeri county, about 130km (80 miles) north of Nairobi.
The elephant was grazing in Mere Forest when it attacked the man, who sustained serious chest injuries, fractured ribs and internal trauma.
He was taken to a nearby hospital where he died from his injuries.
The incidents raise concern over the impact of human-wildlife conflict in Kenya, with many victims' families and organizations calling for compensation.
In 2024 the government launched payment of Sh960 million as compensation to families who suffered injuries, death or damages to food crops and property caused by wildlife.
The payment launched by President William Ruto was set to compensate victims and families of wildlife conflict for their losses and enable them to rebuild their lives.
By May of the said year, human-wildlife cases processed by the County Wildlife Conservation and Compensation Committees across the country had accumulated to about 16,000 claims worth Ksh. 4.5 billion and were awaiting Ministerial Wildlife Conservation and Compensation Committee sittings to be held in the respective Counties.