The occasionally grisly Victorian-era show will end when the second series winds up in just under a fortnight on BBC1.
Actor Jerome Flynn said the cast and team were told this week and were "in a state of a shock".
He revealed the programme was being axed during an interview with presenter Simon Lederman on radio station BBC London 94.9 last night. But he said there was still hope that BBC drama chiefs would change their minds.
The programme - set in late 19th century east London - launched just under a year ago and also stars Matthew Macfadyen.
Flynn said: "We found out this week that the third series of Ripper Street isn't going. We're all in shock.
"It was up against I'm A Celebrity ... Get Me Out Of Here! and that's been cited as one of the reasons in terms of viewing figures.
"We're all in absolute shock because it's a wonderful job and we feel like it's kind of this unfinished work. So we're hoping it will turn around if anyone from the BBC is listening.
"There's these wonderful storylines which Richard (Warlow) and Toby (Finlay), the writers, have marked out and it's one of the most captivating characters I've played and also been part of in terms of the story, so it is suddenly like a marriage being broken," added Flynn
A BBC spokeswoman said: "We are very proud of Ripper Street which has enjoyed two highly ambitious series on BBC1. However, the second series didn't bring the audience we hoped and in order to make room for creative renewal and new ideas it won't be returning."