The Pacific region (Oceania minus Australia/NZ) holds the distinction: ~25% of Earth's land area, but under 0.5% of global population.
Most Pacific Islanders live in Papua New Guinea (~9M), Fiji (~900K), Solomon Islands (~700K). Many microstates have <20K residents.
Antarctica has zero permanent residents—but it's a continent, not a "region" in the inhabited sense. The Pacific is the least peopled inhabited region.