The first Test will begin on September 18 at Galle, but there will be a rest day on September 21 when the voting is set to take place, the board said.
The final match will also be played at Galle from September 26.
New Zealand's last tour of Sri Lanka was in August 2019, when they drew a two-match Test series with the hosts.
Next month's presidential election is the country's first poll since it declared a sovereign default in 2022 during an unprecedented economic crisis.
Months of protests over shortages of food, fuel and medicines forced then-president Gotabaya Rajapaksa to step down after an immense crowd of angry Sri Lankans stormed his compound.
His successor Ranil Wickremesinghe introduced tough austerity measures in line with an IMF rescue package negotiated last year.