Karen Gillan, whose character Amy Pond is leaving during the next series of the sci-fi drama, has played the Eleventh Doctor's assistant since Steven Moffat's 2010 relaunch.
An IGN survey, to which 5,000 users contributed, found that over a quarter of voters want Harry Potter actress Watson to replace Gillan as Matt Smith's sidekick.
New Girl's Zooey Deschanel was the second choice, while Anna Friel came third, Pixie Lott finished fourth and Game Of Thrones star Emilia Clarke made fifth place.
Attack the Block's John Boyega was the highest-ranked male in the poll.
Chris Tilly, entertainment editor at IGN.com, said: "Emma is the overwhelming favorite with viewers - as Hermione Granger she empowered super-smart girls all over the world and she also showed impressive action credentials in the later Harry Potter movies.
"Fans really want to see her make the switch from magic to time travel. With Karen Gillan leaving, this will be one of the most hotly-contested roles in TV."
> Matt Smith on Doctor Who: 'I have no plans to leave'
Watch Karen Gillan talking about her Doctor Who departure below: