The General People's Congress on Saturday said it appointed two members to the posts of vice president and secretary general in place of Hadi, who became president after Saleh was forced to resign in February 2012 after a year of bloody protests.
The UN Security Council a day earlier imposed sanctions on Saleh for threatening the peace and stability of the country and obstructing the political process.
The three men, including military leaders Abd al-Khaliq al-Houthi and Abdullah Yahya al-Hakim, are now subject to a global travel ban and asset freeze.
Saleh denied seeking to destabilise Yemen and his party had warned that any sanctions on the former president or "even waving such a threat would have negative consequences on the political process".
The UN decision came after thousands of Saleh and Houthi supporters filled the streets of Sanaa to protest the move to punish the ex-leader.
"GPC party's sacking of Hadi is obviously the first reaction to UN sanctions against Saleh. But how significant is the decision (remains to be seen)," Al Jazeera's Hashem Ahelbarra, reporting from the capital, said.