Bouchareb filed his resignation with the Bureau of the People’s National Assembly, the legislature said on Facebook.
"The Council’s Bureau unanimously approved the vacant status of the post", the message read.
According to Ennahar TV broadcaster, Bouchareb will be temporarily replaced by lawmaker Terbech Abderazak.
Bouchareb, a long-standing supporter of ex-Algerian President Abdelaziz Bouteflika, stepped down amid ongoing anti-government protests in the county.
An acute political crisis and accompanying demonstrations broke out in Algeria in February after then-president Bouteflika announced his bid to seek a fifth term in office.
Despite the president eventually being pushed out of office, protesters are still demanding that all politicians who got positions in Bouteflika's government resign. Former Algerian Prime Minister Ahmed Ouyahia and several government ministers have been under investigation as part of an anti-corruption crackdown targeting allies of the ousted president.