Congressional aide Barry Nolan says Maloney was resting in a high-altitude camp after a successful ascent to the summit of the world's sixth-highest mountain when he died.
The family was informed early Saturday.
Arrangements are still being made to recover the body from the slopes of Cho Oyu (CHOH' oh-YOO'), a 26,906-foot peak straddling Nepal and Tibet.
Nolan says Rep. Maloney was "very shaken" by the death.