No. Papua New Guinea (PNG) lies 2–11°S of the equator with tropical temperatures year-round. Glaciers require sustained sub-freezing conditions at high elevation.
PNG's highest peak, Mount Wilhelm (4,509 m / 14,793 ft), has perennial snow patches but no true glaciers. The equilibrium line altitude (ELA) in this latitude is ~5,000+ m—above PNG's highest summits.
Nearest glaciers: Puncak Jaya (Carstensz Pyramid, 4,884 m) in Indonesian Papua (Western New Guinea), which retains small ice caps rapidly disappearing due to climate change.