The incident occurred on Tuesday in Depalpur sub- division, located 80 km from Lahore, the capital of Punjab province.
The barber, Muhammad Yousuf, had reportedly developed relations with a married woman who lived in his neighbourhood.
On Tuesday, Nasim Bibi, a relative of the married woman, asked Yousuf to meet her at a place where several men overpowered the barber and chopped off his nose, lips and tongue. They also tried to gouge out his eyes.
Yousuf was rushed Mayo Hospital in Lahore, where doctors described his condition as critical.
Okara district police chief Usman Gondal said five men had been arrested so far and police were conducting raids to nab two more men.
Punjab Chief Minister Shahbaz Sharif visited the hospital and gave a cheque for Rs 500,000 to Yousuf.