Former skipper Nili Latu was omitted from the squad after Maka was instructed to leave him out by officials.
The prospect of Latu being named had led to the resignation of Tonga Rugby Union chairman Bob Tuckey after Latu had not played in any of the warm-up games.
New chairman Reverend Tevita Latailakepa said it was not appropriate for the player to be included in the squad.
The party includes vice captain Vungakoto Lilo of Bristol, Worcester hooker Aleki Lutui, Perpignon prop Kisi Pulu and Beziers back-row Samiu Vahafolau amongst its overseas players, as well as the Stade Toulouse-based Maka.
Tonga will take on hosts New Zealand in the opening game of the tournament in Auckland on September 9.
Tonga 30-man squad: Aleki Lutui, Ephraim Taukafa, Aloisio Ma'asi, Alisona Taumalolo, Kisi Pulu, Soane Tonga'uiha, Halani Aulika, Taufa'ao Filise, Kelekolio Hehea, Sione Timani, Tukulua Lokotui, Joseph Tu'ineau, Sione Kalamafoni, Finau Maka (captain), Viliami Ma'afu, Samiu Vahafolau, Sione Vaiomo'unga, Taniela Moa, Thomas Palu, Samisoni Fisilau, Kurt Morath, Siale Piutau, Alipate Fatafehi, Andrew Ma'ilei, Sukanaivalu Hufanga, William Helu, Fetu'u Vainikolo, Alaska Taufa, Viliame Iongi, Vungakoto Lilo.
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