The couple, who announced their engagement on New Year's Eve, clashed at the Wireless Festival in Hyde Park this weekend, having apparently been drinking for around eight hours.
"Rochelle became upset with Marvin," an insider told The Mirror. "She was telling a friend that she was annoyed at him, as he tried to calm her down."
"Later... Rochelle was shouting at him, 'You didn't pick me up'. By this time they were both well watered. They'd been drinking since about two o'clock in the afternoon, and it was now gone 10pm.
"A friend intervened and told them to have it out in private because everybody was looking."
However, a source close to the couple insisted that the fight wasn't "relationship-changing".
"They just had a little disagreement. The wedding's definitely on," the source stated.
It was revealed recently that Humes and Wiseman are to postpone their honeymoon by five months due to work commitments.
Wiseman and fellow Saturdays stars Frankie Sandford, Vanessa White and Mollie King recently served as bridesmaids at the wedding of their bandmate Una Healy and Ben Foden.