Episode one of Doctor Who: The Adventure, which features the voices of Matt Smith and Karen Gillan, has received 524,299 download requests in its first 12 days of availability.
The Doctor Who website hosting the online game has also seen a 67% week-on-week increase in its unique visitor numbers in the UK.
Simon Nelson, head of the BBC's multiplatform in vision team, said that he is "thrilled" to gain over half a million downloads for the episode in such a short time.
Nelson said that the project has been a "real labour of love" and so he is glad to receive "universal praise" from the Doctor Who fans.
"It's clear we've got people playing these interactive episodes who wouldn't ordinarily play through a computer game - and the opportunity to actually be the Doctor is hugely appealing," he said.
"Whilst the 67% increase in UK visitors to the Doctor Who website is a combination of factors - not least the excellent Vincent Van Gogh section which complements episode 10 - the adventure games page was a significant destination."
On June 22, Doctor Who writer Steven Moffat will unveil the game's second episode at a BBC Learning evening in Scotland. The new episode will apparently feature "some of the Doctor's most fearsome enemies".
Moffat said that the way the game has captured the look and feel of the science fiction television series is "amazing".
"Matt Smith walks like a drunken giraffe on-screen and also in-game - it's a virtuoso virtual performance, and one I'm delighted is proving to be so popular. Just worried I won't get any writing done, what with playing the game all the time," he said.
"Karen is a staggering companion - literally, have you seen her when the Tardis shakes? - and her personality is perfectly captured in these episodes. There are some genuinely funny lines between the two, so we've really brought the TV series into the control of families up and down the country. Half a million download requests in 12 days - amazing."