Hadi replaced several top ministers, including the electricity, finance and foreign ministers, last Wednesday amid rising popular discontent driven in part by power cuts and high prices.
He named Ahmed Abdul Qader Shayyeh as oil minister at the same time but Saba reported on Monday that Shayyeh had declined the post on health grounds.
Domestic insurgencies and a nationwide fight against Al Qaeda militants in the country have hit impoverished Yemen's economy, as oil and water resources decline.
Wealthy Gulf neighbours and the West fear for the stability of Yemen, which shares a long border with the world's top oil exporter, Saudi Arabia.
Washington has stepped up support for the government and military at the same time it has launched deadly drone strikes on suspected Islamist militants there..