The 27-year-old actor, who will play the Eleventh Doctor in the new series, said that a scarf he often wore led to friends giving him the nickname.
He told Esquire: "At university I had a big coloured scarf, and people would often say, 'Alright, Doctor Who?' And I thought, I rather liked the notion."
Smith also admitted that his mum encouraged him to audition for the part when she suggested he would make a good Time Lord after discovering that David Tennant would be departing the role.
Smith's 'Who' audition was 'silly, crazy'
Matt Smith has revealed that he tried to make his Doctor Who audition "crazy" and "silly".
Speaking to Esquire magazine, the 27-year-old actor likened the role to playing Hamlet.
"I tried to make it as funny as it should be but it's a bit like playing Hamlet," he said. "It has to be your version. The Doctor is so committed, whoever plays him.
"So I tried to be creative and artistic, and silly, and crazy, and also the cleverest man in the world, and part of that is there's a rapidity to the way he speaks."
He added: "He's an intergalactic genius, a superhero-ish, mad, fumbling, bumbling, science geek. He's everything you can pluck from any universe and put into him."Source: Digital Spy