Reza Gul, 20, was rushed to hospital after the attack in Ghormach district in the northwestern province of Faryab on Sunday. Her husband is said to have fled to a Taliban-controlled area.
"Mohammad Khan (the husband) cut off Reza Gul's nose with a pocket knife," Faryab governor's spokesman Ahmad Javed Bedar told AFP.
The incident highlights the endemic violence against women in Afghan society, despite reforms since the hardline Taliban Islamist regime was ousted by a 2001 US-led invasion.
"Such incidents would not happen if the government judicial system severely punished attacks on women," added Alema, who goes by one name.
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The disfigured woman's photograph was widely shared on social media, prompting calls for tough action against the husband.
Bedar said Gul would need reconstructive surgery, which was not possible in the local government hospital.
It was not immediately clear what prompted the husband to attack Gul, the mother of a one-year-old child who was married off five years ago as a teenager.
The government has vowed to protect women's rights but that has not prevented deadly attacks.
In November a young woman was stoned to death after being accused of adultery in the central province of Ghor.
And last March a woman named Farkhunda was savagely beaten and set ablaze in central Kabul after being falsely accused of burning a Koran.
The mob killing triggered angry protests nationwide and drew global attention to the treatment of Afghan women.
The cover provoked a worldwide outpouring of sympathy for Aisha, who was taken to the United States where she was given a prosthetic nose.