As the Tongan team cut their squad to 19 on Monday, the loss of Jennings was the biggest blow.
The forced withdrawal of the 31-year-old who has played 10 Tests for Tonga and seven for Australia leaves Solomone Kata (Warriors) and Kotoni Staggs (Broncos) as the logical choices to play in the centres in Auckland on Saturday.
"It is a shame to lose Michael because he has really been playing well for Parramatta," Mate Ma'a Tonga coach Kristian Woolf said.
"He has also brought wonderful experience to our side through the 2017 World Cup and in Tests last year.
"But we have some quality centres in our squad in Solomone Kata and Kotoni Staggs, so I know we can fill the hole left by Michael's injury."
Jennings' brother Robert and Gold Coast prop Moeaki Fotuaika were the other players omitted as the squad was cut from 22 to 19. The Titans on Monday announced that Fotuaika has a wrist injury.
The 17-man squad that will contest the Test will be named on Tuesday.
Tonga will also await the fate of prop Andrew Fifita at the NRL judiciary when he attempts to have a dangerous contact charge downgraded.
If unsuccessful, Fifita will miss the Test and the next two Sharks matches
Mate Ma’a Tonga squad
John Asiata (North Queensland Cowboys)
Manase Fainu (Manly Sea Eagles)
Andrew Fifita (Cronulla Sharks)
Addin Fonua-Blake (Manly Sea Eagles)
David Fusi'tua (New Zealand Warriors)
Siliva Havili (Canberra Raiders)
Tuimoala Lolohea (Leeds Rhinos)
Will Hopoate (Canterbury Bulldogs)
Solomone Kata (New Zealand Warriors)
Sione Katoa (Penrith Panthers)
Manu Ma'u (Parramatta Eels)
Tevita Pangai Junior (Brisbane Broncos)
Kotoni Staggs (Brisbane Broncos)
Tevita (Junior) Tatola (South Sydney Rabbitohs)
Sio Siua Taukeiaho (Sydney Roosters)
Jason Taumalolo (North Queensland Cowboys)
Peni Terepo (Parramatta Eels)
Daniel Tupou (Sydney Roosters)
Sitili Tupouniua (Sydney Roosters)