The video, on the Mail Online website, appears to have been filmed by Doncaster-born Louis Tomlinson during their tour in Peru and seems to show him sharing a joint with bandmate Zayn Malik, from Bradford.
Tomlinson can be clearly heard saying: “So here we are, leaving Peru. Joint lit. Happy days!”
At one point smoke is seen being blown across the car
A motorcycle police officer drives past and Tomlinson says: “He’s having a look. He’s thinking ‘I’m sure I can smell an illegal substance in there’. And he’s hit the nail on the head.”
Tomlinson and Malik are also heard joking about “illegal substances” as they smoke in the back of a car.
A spokesman for the band, who start the mainland UK leg of their Where We Are world tour in Sunderland tonight, said: “This matter is in the hands of our lawyers.”
Thousands of fans took to Twitter to defend the clean-cut band with one who tweets as voguemalik saying: “Zayn and Louis are both in their 20s. They are old enough to take care of themselves and do what they want.”
Another fan, called cuddleharold, said: “Smoking weed doesn’t make you a bad person but the media is gonna blow this up way out of proportion and I feel bad for Zayn and Louis”.
The band, who have a huge following on social media, rose to fame as teenagers on ITV’s The X Factor talent show and have become one of Britain’s biggest bands, with a huge and loyal following of young girls across the world.
Other band members Harry Styles, Liam Payne, and Niall Horan are believed to have been travelling in different cars and were not seen in the video.
Earlier this month, the band were named fourth in the Sunday Times Rich List of young musicians with an estimated fortune of £14 million each and a combined wealth of £70 million.