The accident occurred in the Kibwezi area around midnight local time on Monday as the bus driver was trying to overtake another vehicle but collided with the oncoming tanker truck, Kibwezi police chief Leonard Kimaiyo told Reuters by telephone.
"Twenty adults and three children died on the spot, while one adult died later in hospital," Kimaiyo said.
The bus was heading to Mombasa from Nairobi. Kimaiyo said most of the passengers were families returning from Easter festivities and students preparing for the reopening of schools after holidays.
Another 19 people were injured. Kimaiyo said the death toll could rise.