A federal judge on Monday denied prosecutors' request to jail money manager Bernard Madoff for allegedly violating a court order by mailing more than $1 million worth of valuables to friends and family.

Instead, the judge ruled that Mr. Madoff, who is accused of running a Ponzi scheme that cost investors tens of billions of dollars, can remain free but must give the government an inventory of his transportable valuables and let a private security company regularly check that the items are still in his possession and search...