The government defended the proposal, saying the capital Nairobi's airport was operating beyond its capacity and private investment was needed to upgrade it.
Dozens of airport workers blew plastic trumpets and chanted, “Adani must go,” on Wednesday morning, according to footage broadcast by local broadcaster Citizen TV.
The footage also shows police officers beating protesters with batons.
Wilma van Altena, who was on holiday in Kenya but had to end her trip early to return to the Netherlands to attend a funeral, was also stuck at the airport.
“It was chaotic… when we arrived there were hundreds of people outside the airport and we were standing around before we were finally allowed in,” she told the BBC.
“We have no information. There's nothing on the bulletin boards, no word from the airlines. We have to go home, but we have no idea when that will be.”
The Zimbabwe men's soccer team was also stranded.
An unnamed official told the BBC that the team had arrived in Nairobi after playing an Africa Cup of Nations qualifier in Uganda, but no information had been provided about a follow-on flight to Harare.
The BBC's Stuart McLean, one of those waiting for the flight, said hundreds of people queuing outside the airport at around 5:45 a.m. BST (7:45 a.m. local time) were calm and patient, but frustrated.
He said the cabin crew and pilot were also waiting.
Kenya Airports Authority said it resumed “minimal operations” at 5am BST (7am local time), adding that it was working with the relevant parties to resolve the disruption.
Kenya Airways CEO Allan Kilavuka told the BBC that only a third of scheduled flights had taken off on Wednesday morning.
Workers at other airports across the country also joined the strike.
Kenya's aviation workers' union has threatened an indefinite strike after the government failed to disclose details of a deal with Adani Group, one of India's largest conglomerates.
The Kenya Bar Association and the Kenya Human Rights Commission also criticized the plan, saying it was unfair to lease the country's strategic assets to a private company.
Both parties appealed to the High Court, which subsequently stayed the deal to allow time for a judicial review.
A final court ruling date has not yet been set.
