The cabinet which met under the chairmanship of President Uhuru Kenyatta, directed the formation of an experts committee to monitor the country on a 24-hour basis on any signs of the disease, Xinhua reported.
The cabinet, which met in Nairobi, also directed the ministry of health to set up an Ebola response team in the event of an outbreak.
"The cabinet expressed satisfaction with the measures taken and urged Kenyans to remain fully alert everywhere as a way of ensuring our country remains free from the disease," a statement said.
So far, Kenya Medical Research Institute (KEMRI) has tested at least 36 alert cases, all of which negative to Ebola.
KEMRI is a World Health Organisation (WHO)-recognised laboratory for testing and confirming Ebola cases. It has capacity to serve the sub-region.
"To ensure there are no infections in the country, the government has ordered the 100 percent screening of all air passengers entering Kenyan soil," the statement said.
The statement noted that 11 scanners have already been installed at major airports. More will be installed in coming days.
It said the construction of an isolation facility at the Kenyatta National Hospital, the largest referral hospital in Kenya, which has been set aside as a temporary isolation facility is almost complete, other two facilities are under construction in two other hospitals.
The cabinet said 10,000 people have already been trained to provide help in managing the disease and prepare for any eventuality.
The measures come as the World Bank Group on Thursday announced an additional $100 million funding in its Ebola crisis response to speed up deployment of foreign health workers to the three worst-affected countries in West Africa.
West Africa and global development leaders have in recent weeks appealed for a massive coordinated reinforcement of international health teams to the three countries in order to contain the epidemic.
Kenya requires about $20 million for the programme of tackling Ebola and so far the government has set aside $7.5 million and also received $2.7 million for the project from the World Bank.
At least 600 Kenyans have volunteered to travel to West African countries to support in tackling the Ebola outbreak, according to Kenya's director of medical services Nicholas Muraguri.