Miranda, a Brazilian national, spent almost nine hours in detention under British anti-terror legislation on Sunday as he passed through London Heathrow Airport en route from Berlin to Rio de Janeiro.
British police confiscated some of Miranda's electronic equipment including his mobile phone, laptop, camera, memory sticks, DVDs and games consoles, according to The Guardian.
The Guardian itself was not taking legal action, Rusbridger said.
"At the moment this is a legal challenge by David Miranda, who is the individual, and he has lawyers who will mount that challenge," the editor said.
"He wants that material back and he doesn't want it copied."