Officers in the Taleban militia have arrested 28 barbers across the city of Kabul.
He added that the barbers were accused of popularising anti-Islamic western hairstyles.
The BBC's Kate Clark in Kabul said barbers had been sent a letter from the Taleban religious police warning them not to give "foreign haircuts".
Titanic craze
She said: "Specifically outlawed are what are called the English cut and the Beatles cut - a reference to the long hair of the British pop group - and a cut inspired by DiCaprio."
The Titanic style, with a long fringe and cropped back, became popular when copies of the movie, which is banned in Afghanistan, were circulated on video tapes.
A Titanic craze swept Kabul in November last year, with wedding cakes in the shape of the ship becoming extremely popular.
"We are very nervous to accept orders for this hairstyle anymore. So are the youth," said a barber who asked not to be named.
Several young men have visited his shop to have their haircuts corrected in line with the Taleban's military style, he added.
Ill-fated ship
The Taleban movement seized control of Kabul in 1996, imposing a strict version of Islamic Sharia law which bans music and television and enforces dress codes for men and women.
Kate Clark said: "Fringes, quiffs, close-cropped sides - all are unacceptable for the Taleban.
"The religious police say Muslim men should have evenly-cut hair, either closely cropped or reaching the ear lobe, jaw or shoulder, with a centre parting and a full and untrimmed beard.
"That, they say, is following the example of the prophet Mohammed."
The men arrested have been allowed visitors but the Taleban religious police have the power to administer short jail sentences and give religious instruction without the offender receiving a court trial.
Titanic has left a lasting impression on film fans in Kabul.
It is one of the biggest-grossing movies of all time and has taken more than $1.8bn (£1.2bn) since it was released in 1997.