The pair went to Puero Rico together last month to film sequences for Q'Viva! The Chosen, their multi-country take on the reality/competition format.
Despite having split since conceiving the show, on that trip the producers and hosts seemed amicable and determined to continue the project as a team.
But since the emergence of Lopez's relationship with back-up dancer Casper Smart, including taking him on a holiday with their twins, they have not been seen together.
Instead, over the last week J-Lo has been shooting the show in various Latin American countries without Anthony.
After a couple of days in Peru, she was pictured arriving in Chile with Smart.
According to a US magazine, Anthony refused to work with her after the pair had a blow-up last week while she was in Morocco with the dancer.
A source told Star magazine: 'Marc and J.Lo had a tense conference call while she was in Morocco.
'Inevitably, the discussion boiled down to her new boyfriend (Smart) and Marc made the decision not to work with Jennifer last week as a result.'
After seven years of marriage, Lopez and Anthony announced they were splitting up in July. They are parents to three-year-old twins Max and Emme.