People.com said Prince Michael, 16, was booked to appear on an episode of the German TV interview and game show "Wetten, dass?" which was to tape in Mallorca, Spain.
However, a spokeswoman at the German TV station ZDF said Thursday he dropped out at the last minute.
"Under these circumstances, we perfectly understand that Prince Michael prefers to stay close to his family. We wish Paris the strength and the power to recover soon," station representative Silke Blomer told People.com.
Paris, 15, cut her forearm with a meat cleaver and took numerous Motrin pills before she was hospitalized early Wednesday, TMZ said.
A source identified as close to Paris told the celebrity news website this is not the first time the troubled child has attempted to take her own life.
TMZ said the youth received stitches to close the wounds and is expected to recover from her injuries.
Paris, Prince Michael and 11-year-old Blanket are the children of Michael Jackson, the pop star who died June 25, 2011, after his personal physician accidentally administered a lethal amount of sedatives and anesthesia to help him sleep. He was 50.
Paris and her two brothers have been living with their paternal grandmother Katherine since their father died. The teens have both expressed interest in working in the entertainment industry.