Writer Oriane Messina confirmed the show's axe on Twitter, blaming the cancellation on disappointing audience numbers.
"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: