Skinner - who joined the show in 2011 - will take up a new position at BBC Drama Production in London.
"It has been an honour to have been a part of Doctor Who, and a privilege to have worked with Steven Moffat and Matt Smith on this extraordinary show," she said in a statement.
"I have hugely enjoyed my time in BBC Wales and would like to thank [BBC Wales' Head of Drama] Faith Penhale, and our wonderful production team for their unending commitment and brilliance.
"I will miss them all enormously, but I'm leaving Doctor Who in fine form, with the new series starting at Easter and the fantastic plans for the 50th Anniversary already underway."
Skinner added that she is "delighted" with her new BBC Drama role and is looking forward to "the new opportunities and projects that [the position] will bring".
Faith Penhale will now serve as Doctor Who's executive producer for the show's 50th anniversary special alongside showrunner Steven Moffat.
Doctor Who returns to BBC One with new episodes from Saturday, March 30.
> Doctor Who returns: Clara, Ice Warriors, guest stars - new pictures
Watch a trailer for Doctor Who's new episodes below: