Those that submitted the footage would have a chance of appearing in the band's upcoming film, Sky News reported.
The band tweeted: "Have a real #1D tattoo? Show us! Submit a 90 sec YouTube video to firstname.lastname@example.org and show us why you should be in the @1D3Dmovie!"
"This tweet was posted in error and has now been removed. One Direction do not want to encourage any of their fans to get 1D tattoos."
Many objected to the request, which was posted on Facebook and Twitter, as many that follow the band are under the age of 18.
"Okay One Direction, I love you guys to pieces I really do, but promoting young girls to get a tattoo?," Julia Zwagerman, a Facebook fan of the group, said of the request.
Some members of the band have recently begun displaying hipster tattoos on their bodies, Sky News reported.