Attorney Ira Sorkin said Madoff made the decision out of consideration for his daughter-in-law's and grandchildren's privacy.
Sorkin said Monday that Madoff, 72, will conduct a private service at the North Carolina prison where he's serving a 150-year term.
Mark Madoff, Bernard Madoff's eldest son, hanged himself on Saturday in his New York City apartment.
The 46-year-old killed himself on the two year anniversary of his father's arrest for cheating thousands of investors of billions of dollars in a Ponzi scheme.
The Associated Press contributed to this report.