The move comes as rising energy, insurance and staffing costs lead to a $30m funding gap.
Te Papa will begin charging an entry fee for international visitors from September.
Entry to the museum will remain free for New Zealanders.
The entry fee will be $35 and will apply from 17 September to international visitors aged 16 years and older.
With nearly 600,000 international visitors in the 2023/2024 financial year, Te Papa is expected to earn an additional $5-$10 million per year from the move.
Johnston said visitors would self-identify their nationality.
"You'll walk into Te Papa and we'll say, 'Kia ora, how are you? Where have you come from today?' And if you say, 'Oh, I've come from Johnsonville', then we'll say, 'Great, head up the stairs, head into the museum, have a wonderful visit'.
"And if you say, 'Oh, I'm from France' or 'I'm from Germany', we'll say, 'Awesome, head up the stairs, you'll see the ticket desk right there, that's where you can buy your ticket'."
I'm curious, who here would pay $35 to visit Te Papa? I haven't been there in years, and I work in Wellington, I could just drop in after work.
Also, the fact they don't actually check if someone's from NZ or not beyond asking will spread quite fast, and I suspect a large chunk of visitors will say where they're staying in NZ, rather than their country of origin.
If I was visiting say London, and went to a museum, I'd think nothing of paying $35NZD to enter. People expect to spend money on holidays.
I also think most people would pay if they were supposed to. You don't spend thousands to travel across the world then go out of your way to avoid paying $35. You just pay it. Or at least I would.