The 35-year-old Odumbe, who picked up an injury against India 'A' last Saturday and missed the last two matches, will play no further part in the series as his suspension takes immediate effect.
Local cricket observers have voiced their concern that without Odumbe, the national team, which is preparing for the ICC Champions Trophy in England next month, would badly be weakened.
The player was also named in the 14-man squad for the second biggest cricket tournament that starts on September 10.
"The team is done," said Kenyan cricket analyst Richard Mwangi. "There is no replacement for Odumbe in the team. He's an off-spinner, a batsman and a brilliant fielder."
Despite Odumbe's wish to appeal, the Kenya Cricket Association (KCA) has put four players on standby as his replacement.
They include leg-spinner Collins Obuya, who is recuperating after surgery and the discarded left-arm spinner Brijal Patel.