Madoff, the son of disgraced financier Bernard Madoff, left behind four children - an 18- and 16-year-old from a previous marriage and a 4- and 2-year-old with wife Stephanie Madoff.
"Regardless of what you feel about my father-in-law and his monstrous crimes, Mark's children are innocent victims and this is tragic for them," Stephanie Madoff said in a statement, her first remarks since the death on Saturday.
"I am devastated and now raising two small children alone," she said. "I ask that you please show decency and understanding toward all of Mark's children and allow us to mourn in private."
Stephanie Madoff said her husband's body had been cremated and that there would be a private gathering honoring him later this week at an undisclosed location.
"I deeply appreciate the expressions of heartfelt sympathy and support I have received over the past several days from so many people who knew and loved Mark," she said. "I will miss him and love him forever."
Madoff, 46, hanged himself with a black dog leash in his Manhattan apartment on the second anniversary of his father's arrest on charges he cheated thousands of investors out of tens of billions of dollars.
The suicide came while the Madoff family faced mounting pressure from a court-appointed trustee trying to recover money for victims of the massive Ponzi scheme by filing dozens of lawsuits to meet a deadline.
The trustee and federal investigators have been trying to determine if Mark Madoff - along with his brother, Andrew Madoff, and his uncle Peter Madoff - participated in or knew about the fraud. The brother and sons, who held management positions at the family investment firm, have denied wrongdoing.
Bernard Madoff's attorney has said he will mourn privately at the North Carolina prison where he's serving a 150-year sentence.