The video, appears to have been filmed by Louis Tomlinson during their tour in Peru and seems to show him sharing a joint with bandmate Zayn Malik.
Tomlinson can be heard saying: "So here we are, leaving Peru. Joint lit. Happy days!"
At one point on the video smoke is seen being blown across the car.
A spokesman for the band said yesterday: "This matter is in the hands of our lawyers."
Thousands of fans took to Twitter to defend the 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."