Mason injured himself playing a warm-up game on Saturday and failed to recover in time for the opening Test in Christchurch.
He joins Kyle Mills and Scott Styris as the third casualty in a New Zealand team bracing themselves for a tough two-match series.
Sri Lanka have never won a series in New Zealand and rarely win away from the sub-continent but have been in good form this year.
They drew 1-1 in England then beat South Africa 2-0 at home with Kumar Sangakkara and Mahela Jayawardene sharing a world record partnership of 624 runs and all of their batsmen made a least 50 in their warm-up match with Otago.
"Everyone's in form I reckon, it's just a matter of adapting pretty quickly to different conditions to what we've been playing in," Sangakkara told the New Zealand Press Association.
"With the volume of cricket we've played and the conditions we've been through, we've adapted very well. Right now the guys have no complaints."
Bowlers Muttiah Muralitharan and Chaminda Vaas both missed the practice match to save themselves for the Test but there is some concern about unorthodox paceman Lasith Malinga after he skipped a training session.
New Zealand have not played a Test since losing in South Africa in April and skipper Stephen Fleming said there was a risk his side might be underdone.
"It gives them an edge we haven't got. They're in form, they've played better cricket and more of it," Fleming said.
The absence of Mills and Styris forced the New Zealand selectors to recall batsman Mathew Sinclair and specialist opener Craig Cumming.
New Zealand coach John Bracewell said Sinclair was recalled because of his consistent performances in first-class cricket, while Cumming was included because the Kiwis wanted a specialist opener after experimenting with different players.
New Zealand: Stephen Fleming (capt), Craig Cumming, Jamie How, Mathew Sinclair, Nathan Astle, Jacob Oram, Brendon McCullum (wk), Daniel Vettori, James Franklin, Shane Bond, Chris Martin and Ian O'Brien.
Sri Lanka: Mahela Jayawardene (capt), Kumar Sangakkara (wk), Sanath Jayasuriya, Upul Tharanga, Tillakaratne Dilshan, Chamara Kapugedera, Chamara Silva, Prasanna Jayawardene, Farvez Maharoof, Chaminda Vaas, Lasith Malinga, Dilhara Fernando, Akalanka Ganegama and Muttiah Muralitharan.