Selectors believe Odoyo would not have recovered sufficiently from a knee operation he underwent in Nairobi last month.
With an eye on the future, the selectors have included three members of the under-19 national team, wicketkeeper Maurice Ouma, Alfred Luseno and Rageb Aga.
Kenya play the first match of the two-month tour against West Indies 'B' at St. Kitts on January 6 and will also face Trinidad and Tobago, Barbados, Guyana, Jamaica and Antigua.
"It's going to be an educational tour, considering the players will compete in the longer version of four-day matches," Kenya Cricket Association (KCA) chairman of selectors, Harilal Shah, said on Monday.
"Their performance will be keenly watched in the light of the country gaining Test status in a few years time," said Shah, the former national team captain.
The others members of the squad are captain Steve Tikolo, Martin Suji, Kennedy Obuya, Ravindu Shah, Maurice Odumbe, Hitesh Modi, Collins Obuya, Peter Ongondo, Brijal Patel, Lamech Onyango and Francis Otieno.