The person who died in New Mexico was a resident of Lea County, about 50 miles (80km) from Gaines County, Texas, where the outbreak appears to be centred.
Officials did not provide the person's sex or age.
Every one in five measles cases require hospitalization and about three in 1,000 cases result in death, the New Mexico health department said on Thursday.
The current outbreak killed a healthy but unvaccinated six-year-old in Texas, state officials said on 27 Feb.
While the disease was declared eliminated 25 years ago, the US often sees outbreaks, which are defined as three or more related cases.
Still, the two deaths are jarring to many in a country that, before last week, had not recorded anyone killed by measles since 2015. The 2015 death was the first one attributed to measles in the US since 2003.
Three months into 2025, the total number of reported infections in the US has already climbed above 220. There were 285 cases over the entire year of 2024, according to the Centers for Disease Control (CDC).
The CDC has said it is monitoring the current outbreak, which is believed to have started in a rural Mennonite community in Texas with low vaccination rates.
While the outbreak is mostly occurring in Texas and New Mexico, measles has also recently been found in Alaska, California, Florida, Georgia, Kentucky, New Jersey, New York, Pennsylvania, Rhode Island, and Washington according to the CDC.
Canada is also seeing a spike in infections, and recorded more cases in the first two months of this year than in all of 2024, the country's Chief Public Health Officer Theresa Tam said on Thursday.
Measles has been found in Ontario, Quebec and British Columbia, which Dr Tam attributed to travellers who were exposed to the disease in another country.
As of Thursday, there were 227 measles cases reported this year in Canada and most of those who became ill were not vaccinated, according to the country's public health agency.
The MMR vaccine is the most effective way to fight off the dangerous virus, which can lead to pneumonia, brain swelling and death. The jabs are 97% effective and they also immunize people against mumps and rubella.
US Health and Human Services Secretary Robert F Kennedy Jr - who is known in part for being a vaccine sceptic - published an editorial on Sunday expressing his concern about the growing measles outbreak.
"Vaccines not only protect individual children from measles, but also contribute to community immunity, protecting those who are unable to be vaccinate due to medical reasons," he wrote in Fox News Op-Ed.
