Writer Oriane Messina confirmed the show's axe on Twitter, blaming the cancellation on disappointing audience numbers.
© BBC / Hartswood Films/Laurence Cedrowicz
"We just didn't get the ratings we needed," Messina wrote. "Tough time slot didn't help but we know lots of you loved it."
Me & Mrs Jones starred Sarah Alexander as single mother Gemma Jones, with Neil Morrissey, Nathaniel Parker and Robert Sheehan playing the three men in her life.
In a message to the show's fans, Messina added: "Your support has been amazing, making the show trend and being so loyal, thank you. BBC One is a tough nut to crack."
The series debuted with 3.13m viewers in October, but ratings had fallen to just 1.72m by the final episode.
Neil Morrissey - who played Gemma's ex-husband Jason - previously told Digital Spy that he believed Me & Mrs Jones had the potential to become a long-running series.
"I think it's got great family appeal and it seems pretty much relevant to what's going on today with parents in that particular age group, trying to [get] their life back together and having choices, dilemmas," he explained. "It feels good, so I think the public will latch onto it."
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Watch a clip from Me & Mrs Jones below:
