He was due to be sworn in on Sunday in Washington DC, and is the first member of Congress to die from the disease.
The politician announced on December 18 he had tested positive for coronavirus and is not thought to have had any underlying conditions. He is survived by his wife and two young children.
A spokesman for the family said they appreciated “the numerous prayers and support over the past days”.
Among those paying tribute was Louisiana’s Governor John Bel Edwards, who offered condolences “with a heavy heart” and said flags would fly at half-mast on the day of his funeral.
His political opponents in the Democratic Party in the House of Representatives also paid tribute, saying they were “deeply saddened” by his death.
Letlow was a veteran of Louisiana’s political scene, having been chief of staff to former Congressman Ralph Abraham and succeeding him in the seat after he kept a pledge to only serve for three terms.