"A criminal group has been found to plot an attack on Anez," the former opposition senator told reporters at a press conference, as quoted by the Correo del Sur daily.
Murillo did not provide any details of the alleged assassination plot but said he had advised Anez against travelling to the province of Beni, her former constituency, to celebrate her new role.
Anez was a Senate deputy speaker when she took over as interim president last week after President Evo Morales resigned. She was next in line after other senior officials stepped aside.
Morales fled into exile in Mexico after his re-election to a fourth term prompted protests. He asked for political asylum claiming there were plans to kill him. His supporters do not recognize Anez’s mandate and want her to cede power.