The gameshow, hosted by Dermot O'Leary, saw a panel of celebrity guests offering their opinions on disagreements between couples.
However, the series has consistently struggled in the ratings and was moved to a later timeslot, though ITV claimed that had always been planned.
The broadcaster has now decided not to commission a second series of the programme, The Sun says.
"The Marriage Ref is definitely not coming back," a source said. "Ratings were just not strong enough. The figures have to be higher than this for a primetime Saturday night show to work."
The insider added that ITV is "still committed" to O'Leary, who will return to the channel when The X Factor begins later this month.
The Marriage Ref is based on an American format created by Jerry Seinfeld. The show has also been criticised in the US but is currently airing its second season on NBC.