Tarek Saleh, the ex-president's nephew, was "martyred during the confrontation with the militias of treason and backstabbing, the Huthis," read an obituary sent to AFP by the General People's Congress party.
The commander died in hospital after sustaining a shrapnel wound to the liver during the battles that raged between the Huthis and Saleh loyalists in the capital this week, the statement added. It did not elaborate.
The Shiite Huthi rebels on Monday claimed the killing of Ali Abdullah Saleh, two days after he announced he was open to talks with a Saudi-led coalition that has battled the insurgents since 2015.
Clashes between Huthi fighters and Saleh loyalists erupted in Sanaa on Wednesday, with Tarek Saleh's residence one of the first points of conflict in the capital.
For decades bitter enemies, Saleh and the Huthis joined ranks against the coalition for three years, driving Yemen's Saudi-backed government out of the capital and setting up a parallel state.
Their fragile alliance had been unravelling for months, with Saleh slamming the Huthis as "militias" and the rebels accusing Saleh of covert dealings with Saudi Arabia.
The Yemen war has claimed more than 8,750 lives since the Saudi-led coalition joined conflict, triggering what the UN has called the world's worst humanitarian crisis.