Patang lost a vote of confidence by 136 to 60 in the lower house of parliament over accusations of corruption and incompetence in the battle against Taliban insurgents.
"He's lost the vote of confidence and I on behalf of the Wolesi Jirga (parliament's lower house) request the President of the Islamic Republic of Afghanistan to introduce another individual to the parliament for a vote of confidence," said speaker Abdul Rauf Ibrahimi.
Patang, a former deputy interior minister and a career police officer, was dismissed a month after the Afghan government formally took responsibility for nationwide security from US-led NATO troops at a handover ceremony.
But lawmakers approved Mohammadi's nomination a month later as defence minister.
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The cabinet reshuffle at the time was interpreted as an effort by President Hamid Karzai to secure his powerbase before anointing a successor to stand in presidential elections next April.
Karzai has led Afghanistan since the US-led invasion removed the Taliban regime in 2001.
His government has been widely criticised as weak and corrupt, and for failing to address perceptions of worsening security as NATO troops withdraw.