In March, a judge gave Wade until Monday to submit a document indicating justification for his wealth, Africa Review reported. Judge Alioune Ndaw issued the warrant hours after Wade's lawyers submitted the document, court officials said.
Wade's lawyer, Cire Ly, said the 3,000-page document clearly justifies the origins of his client's wealth.
Police arrested Wade at his Dakar residence Monday and took him to headquarters where he remained in custody, Africa Review said.
Wade was a senior minister during his father's rule from 2000 to 2012, and oversaw infrastructure and energy projects.
He is among two dozen former senior government officials being investigated for embezzlement.
Those found guilty face between four and 10 years of imprisonment, court officials said.