Since Capaldi, who currently plays the 12th Doctor, announced on Jo Whiley's Radio 2 show last night that he would be stepping down after Christmas, Piper, 34, said that it would "feel like a snub" if the successive actor was not female.
Speaking to the BBC at the Critics' Circle Theatre Awards in London, Piper said: "I've always supported the original format but I don't know where they can go from here.
"I think it would be great [to have a female Doctor] given the spirit of the world at the moment. I think it would be timely".
However, Piper has ruled out taking on the coveted role herself, adding: "I wouldn't like that responsibility, it's just too enormous, it's so much work.
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Doctor Who: Billie Piper calls for female Time Lord – could she replace Peter Capaldi?
I've always supported the original format but I don't know where they can go from here.
"They have been talking about that since I started, maybe it's one of those things they like to talk about that never comes to fruition, annoyingly," she said.
"I think that would be a welcome turn, they have had a few different age groups and I think that would be the wise way to go. Whether they do actually go that way…
"Although I quite like the traditional format but I don't know how they would move forward with something fresh. I think it would be a wise opportunity."
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Who will replace Peter Capaldi as the next Doctor?
Executive producer Steven Moffat has previously suggested a future regeneration of the character could be a woman, saying: "I think the next time might be a female Doctor. I don't see why not."
Capaldi shocked fans last night when he unexpectedly announced his departure, saying: "I suppose the big thing about it for me is that it will be my last. I will yes. This will be the end for me. I feel sad. I love Doctor Who, it's a fantastic programme to work on.
"It's been a huge pleasure to work with a family. I think Christmas 2017, I've just been told, but I'm still Doctor Who. I've got a lot to do – we're doing epic stuff. I'm not done yet."
Doctor Who returns to BBC One in April.