Twenty five foreign airlines operate out of JKIA, including Kenya Airways, Turkish Airlines, Emirates, South African Airways, and Ethiopian Airlines.
Transport Minister James Macharia said replacement staff had been found to screen passengers and luggage.
"That matter has been sorted out... I can assure you that within the hour we will have our first aircraft actually flying out," Macharia told reporters at 0645 GMT at the airport.
The strike at Jomo Kenyatta International Airport follows a labor dispute over contracts and job security between the Kenya Aviation Workers Union (KAWU) and Kenya Airways.
Kenya Airways CEO Sebastian Mikosz told reporters that 24 flights had been delayed and two diverted to other Kenyan airports.
"We are processing them with the new screeners we have brought in from the air force but also from (Kenya Airways), so the first flight is scheduled for departure at 1030," said Jonny Anderson, CEO of Kenya Airports Authority.
He said there would be delays to scheduled flights throughout the day.
Union leader Moss Ndiema was arrested shortly after making a speech at the airport, Kenya's Citizen TV reported. A court injunction had earlier ordered the suspension of the planned industrial action.
"I feel bad, very bad, because I don't know what is going to happen. There are many passengers here," said Adebukola Idayat Atunrase, an Egypt Air passenger en route to Nigeria.
Source: Reuters