Smith wrote that despite doctors' best efforts, 3-year-old River Kelly Smith was unable to be revived.
The "Backroad Song" singer and his wife Amber decided to say their final goodbyes and donate their son's organs to other children. Smith wrote that he takes solace knowing his son is with God.
"Riv was special," he wrote. "Everyone that met him knew that immediately. The joy he brought to our lives cannot be expressed and his light will be forever in our hearts."
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In lieu of flowers, the family asked for people to donate to Dell Children's Medical Center in Texas in River's name.
Smith, who is signed to Broken Bow Records, has released songs "If The Boot Fits," ''Backroad Song" and "Happens Like That." He and his wife, Amber, also have another son and a daughter.
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The Associated Press contributed to this story.