Pilar Rubio posted a photo of a box containing a gun and bullets and a written message sent to her private Twitter account.
She said she and her son had been targeted by another user who had sent the image along with a number of threats.
Messages sent by the anonymous user included: "Do you want to see how James would look dead?" and "I'm coming to your house now, say goodbye to all your loved ones."
Although Rubio's account is private, the image has since been widely shared online.
FollowJaime F. Macias ✔@JaimefmaciasPilar Rubio, madre de James Rodríguez, denunció, mediante redes sociales, amenazas de muerte contra su hijo.3:12 AM - 10 Oct 2016 3333 Retweets 1616 likes
Pilar Rubio, madre de James Rodríguez, denunció, mediante redes sociales, amenazas de muerte contra su hijo.
The account from which the threats to Colombia international James and his mother were sent was created this month. Twitter has since closed it down.
James was unable to play in Colombia's World Cup qualifiers after suffering a calf strain before Madrid's draw with Eibar, and the Colombian FA said the player would now return to Madrid rather than attending Tuesday's home game against Uruguay.