The actor is a guest in a video featuring characters from the US series and enlists the help of show regular Count Von Count to tackle a tricky problem.
Cumberbatch is set a "brainbending challenge" to demonstrate his skills to young viewers of the long-running educational programme, as he appears without his usual partner in crimefighting, John Watson.
He is given his task by a furry character called Murray-arty who announces "I am your arch nemesis" and asks him to work out whether there are more oranges or more apples laid out in front of him.
Cumberbatch points out he merely portrays the consulting detective and admits: "I'm not really Sherlock, I just play him on the television."
And after being challenged to act like a super-sleuth he concedes "I'm really just an actor," and brings in The Count.
The sketch even apes the recent finale to the BBC1 series in which Moriarty appeared to return, with Murray-arty repeating the line "did you miss me?".
The film was recorded in January and has been posted on YouTube.
You can watch the PBS video here -