The program-producing unit of the NBC network produced the first two seasons. When it was cancelled, the show was sold to Columbia Pictures Television for $60 million. Columbia produced the latter two seasons (though there is a one year interval between them) without NBC's involvement.
Cherie Johnson is the niece of the show's creator and producer, David W. Duclon, who named the character for her. Nevertheless, she auditioned for the role like everyone else and was picked by the network to play the role.
Because the show had many young viewers and was scheduled after football games which tended to run overtime, six fifteen-minute episodes were produced. This was done rather than joining a full-length episode in progress, because that would disappoint children watching the program, and showing it later tended to put them up at a time parents may have considered too late for their children.
During the second season, several of the interiors of the set were altered. The beige couch from the first season was replaced with a blue plaid couch. The bathroom and the hallway were altered, and the front door of Henry's apartment was changed as well.
Although not officially an adaptation, Punky Brewster contains many story elements in common with the novel Silas Marner, in which a miserly old hermit whose only friend is an elderly woman adopts a precocious young girl who was abandoned by her parents.
During the pilot episode, Henry goes out into the rain to look for Punky. After he returns you can see that he never closed his front door when he left. He also never closes the door after returning and putting Punky to bed before retiring to bed himself either.