They had left the capital, Nairobi, and travelled 370km (about 230 miles) west with an empty coffin in the vehicle before being intercepted, the health minister said on Saturday to the BBC.
Nearly two weeks ago, travel in and out of Nairobi was restricted, along with another three regions considered to be coronavirus hot spots.
The group of fake mourners had managed to pass through several checkpoints before suspicious officers in Homa Bay County opened the coffin, Health Minister Mutahi Kagwe said.
The driver later tested positive for Covid-19, the respiratory illness caused by the virus. His three passengers have now been put into quarantine.