Odinga's National Super Alliance said in a statement that the detained man, economist David Ndii, was recently appointed chairman of a committee organising the protest event on December 12.
The statement said police arrested Ndii on Sunday in Diani on Kenya's Indian Ocean coast.
A police official, speaking on the condition of anonymity because he was not authorised to speak to the press, confirmed Ndii is being questioned by detectives.
Odinga successfully challenged President Uhuru Kenyatta's August re-election in court but then boycotted a rerun vote in October, demanding electoral reforms.
Kenyatta won with 98% the votes and was inaugurated last week.