Police in Passaic County, where Pedro Quezada lives and owns a bodega, said they came to his home to tell him that he needed to pay the child support in a "timely matter."
Quezada received his winnings in Tenton on Tuesday, in a lump sum of $152 million after taxes.
Richard Berdnik, Passaic County Sheriff, said that the New Jersey Lottery Division usually pays off a winner's back taxes and child support before they write the check.
But Berdnik said Quezada still owes money to the mother.
"Like everyone else, until this warrant is satisfied, Mr. Quezada is subject to potential arrest," he said.
Quezada has five kids ranging in age from 5 to 23.
When he made a brief public appearance earlier in the week, he told reporters that some of his children live in North Carolina with their mother.
Quezada immigrated from the Dominican Republic 26 years ago. He said he came from a poor family.
In 2009, The Record reported that his bodega burned down. And during that same year, a bank foreclosed on a property he owned.
All Quezada has said about his plans is that he wants to buy a new car and get his wife "whatever she wants."
Their neighbors said they saw the couple moving out of their apartment earlier this week.