Imdad Ali, who is aged around 50, was sentenced to death for the murder of a religious cleric in 2002 and is set to be hanged tomorrow.
HRW opposes the death penalty in all circumstances, its country representative Saroop Ijaz told AFP.
"But in this case it also violates Pakistan's international legal obligations," Ijaz said, referring to the Convention on the Rights of Persons with Disabilities which Islamabad ratified in 2011.
"Imdad (Ali) has no insight into his punishment or condition or the idea of penalty. Executing someone who does not understand the punishment he or she is being awarded is simply harrowing and serves no criminal justice aim."
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"He is a declared insane person," said Tahir Feroze Khan. "To hear about his death warrant is shocking news for me."
A medical report seen by AFP said Ali's speech was incoherent, he frequently spoke and laughed to himself, and he suffered from paranoia and delusions of grandeur.
Despite being officially diagnosed with paranoid schizophrenia, the Lahore High Court last month rejected arguments that Ali should not be executed because of his illness.
"His killing would signify in a grim way all that is wrong with the Pakistani justice system," added Ijaz.
Hangings were initially reinstated only for those convicted of terrorism, but later extended to all capital offences.
The country has executed over 400 people since resuming hangings in December 2014, according to new research by Reprieve, a British anti-death penalty campaign group, although only a tiny fraction have been for terror charges.