The 66-year-old prison governor "on Sunday evening asked the prisoner, who had worked as a hairdresser before being jailed, to come to his office to cut his hair," an interior ministry spokesman told AFP.
The prisoner then used his scissors to stab the prison governor once in the head and then 16 times in his body. The official died before reaching hospital.
The 29-year-old prisoner had been sentenced several months earlier to 17 1/2 years behind bars for murdering a young man, whom he stabbed 57 times.
The mountainous Central Asian country is the poorest former Soviet republic, with around 40 per cent of the population living in poverty.