“This individual has been arrested by Tehran’s cyber police,” the capital’s police chief Hossein Rahimi was quoted as saying by semi-official news agency ISNA.
“We are against this individual and his companion’s norm-breaking and vulgar behaviour and the police and the judiciary will certainly deal with them,” he added, without naming the person who was arrested.
The individual appeared to be Alireza Japalaghy, a Tehran-based parkour athlete with more than 133,000 followers on Instagram.
Parkour is an extreme sport born in France in the 1990s that combines the efficiency of movement across the urban landscape with death-defying leaps.
It has a following in neighbourhoods of west Tehran, where high-rise residential buildings are closely connected.
Japalaghy had posted a series of photos and videos last week showing him and an unidentified woman in revealing outfits hanging off buildings and kissing.
Under the Islamic dress code, women can only show their face, hands and feet in public and are supposed to wear only modest colours.
In an Instagram video on Monday, he said he had received “suspicious calls” telling him to turn himself in or be arrested publicly.
His brother posted an update on the same account the next day, saying Alireza had been taken from their home and arrested.
According to police chief Rahimi, the woman in Japalaghy’s photos “will also be arrested soon”.