Magistrate S. Allan Alexander said she denied bail to James Everett Dutschke because he could be a danger to the community and could attempt to flee, CNN reported.
A preliminary hearing on the charges will be held Thursday.
Dutschke, 41, of Tupelo was arrested Saturday by federal authorities on charges of possessing and sending ricin to Obama, Mississippi Sen. Roger Wicker and Judge Sadie Holland.
The toxin-tainted letters arrived April 16 in the wake of the bombings at the Boston Marathon.
Police had earlier arrested Paul Kevin Curtis of Corinth, Miss. He denied sending the letters and accused Dutschke of framing him.