The baby died January 2nd. It was the first whooping cough death in the state since 1998.
The agency said Tuesday that tests are being conducted on people who had close contacts with the child. Those people are being offered preventive medication.
There were 183 cases of whooping cough in 17 New Mexico counties last year.
Whooping cough, also known as pertussis, is a bacterial infection that at first seems like a cold.
Coughing fits begin a week or two later, up to 15 coughs in a row followed by a high-pitched "whoop" as patients gasp for air.
Infants are more likely to turn bluish than whoop as they run out of air. They can get pneumonia and become dehydrated and malnourished.
State epidemiologist Mack Sewell says the death points to the need to protect very young children from exposure to the bacterial respiratory infection.
Sewell says that before vaccinations were common, young children suffered a high mortality rate from whooping cough.
He says immunizations have reduced that rate and the disease now is more common in teenagers and adults.
Sewell says those cases often go unrecognized because symptoms are milder.
Children are immunized in a series of doses at two, four and six months, between 15 and 18 months and around age four.
Read more information on whooping cough from the CDC