The former Joan of Arcadia star, who plays medical student Martha Masters, originally joined the series as a temporary replacement for Olivia Wilde's Thirteen.
David Shore told TVLine: "I wish [Amber] was sticking around, because she's wonderful, but she's not going to be with us for [much longer]."
He added that Masters will briefly cross paths with her predecessor when Thirteen returns to Princeton-Plainsboro.
"We're going to give her a good send-off," said the producer. "I'm not at liberty to discuss any details, but she's getting a good send-off."
Shore had previously hinted that he would like Tamblyn to remain on the show permanently.
House returns to Fox on January 17.