The Rebel Heart singer mentioned Rocco during a Friday night tour stop in Auckland, New Zealand, according to video obtained by TMZ, and became visibly overwhelmed.
"There's no love stronger than a mother for her son, and if I talk about him too much, I'm going to cry," she told the crowd, before saying she would dedicate her next song, "La Vie en Rose," to Rocco.
"I hope he hears this somewhere and he knows how much I miss him," she said.
Madonna, 57, and Ritchie, 47, have sparred for months over their son. At a New York Supreme Court hearing on Wednesday, the exes' lawyers, Rocco's court-appointed attorney and the judge agreed that the 15-year-old will remain in London with his father, as they work toward settling the custody dispute out of court.
Since leaving his mom's tour in December, Rocco has been living with his father and attending school in London, despite a judge's order for Ritchie to return the boy to New York by January.
A Ritchie source told PEOPLE on Friday that the director "expects the saga to be resolved imminently."
The exes, who divorced in 2008, have disagreed over the proper parenting style for their teenage son, sources with both parties told PEOPLE.
"[Rocco] has been photographed by paparazzi smoking suspicious cigarettes multiple times, has broken his wrist, shaved his head and been without supervision for days at a time," a Madonna source told PEOPLE after the Wednesday hearing, adding, "Madonna sees the damage that's being done to Rocco, who has so much potential, which by his father's influence is now being wasted and destroyed due to lack of guidance from [Ritchie]."
But a Ritchie source said, "He wants Rocco to have the confidence he lacked growing up and thinks Madonna's stern parental style is counterproductive. The welfare of Rocco is Guy's priority."
While Rocco's custody remains unresolved, another court date has been tentatively scheduled for June 1.