The episodes in question, from 1977 serial The Talons of Weng-Chiang starring Tom Baker, have long faced criticism for perceived racism - such as the inclusion of a white actor playing a Chinese character and the use of racial slurs.
After the suitability of continuing to host these episodes on the service was called into question by viewers, they now contain a warning which reads: "contains stereotypes that some may find offensive."
Screenwriter and spokeswoman for British East Asians in Screen & Theatre Emma Ko told The Times earlier this month that the episodes were "really hard to watch because yellowface is so unacceptable now".
Ko also said that for fans who had had similar slurs aimed at them in childhood, "it is so hard to hear that word and not feel immediately a trigger reaction of how wrong it is."
BritBox was launched in 2019 and currently contains a range of British TV shows from both the BBC and ITV, with shows from Channel 4 set to follow in the future.
Amongst its impressive catalogue – which includes the highest number of British boxsets of any streaming service – the platform boasts every classic episode of Doctor Who.
The Talons of Weng-Chiang is the subject of a discussion which will focus on the representation of ethnicity on archive TV at the BFI, which is scheduled for this Saturday – with panelists including Samira Ahmed, Kevin Fong and Emma Ko.
A BritBox source told RadioTimes.com, "BritBox provides a wide variety of programming from different decades for our subscribers to choose from.
"Some of this content reflects the times and attitudes of the time in which these programmes were made.
"Appropriate warnings are on the site to flag sensitive material and enable our subscribers to make their own choices as to what they watch.