The exact cause of the death is under investigation, local media reported on Sunday.
US website Axios, which first reported the news, said Kennedy's trip was arranged after he was informed of the death.
NBC News said Kennedy planned to attend the funeral scheduled for Sunday.
The US Department of Health and Human Services did not immediately respond to a Reuters request for comment.
Kennedy, a longtime vaccine sceptic, said in his immediate response to the first measles death in February that such outbreaks were commonplace.
Many people opposed to vaccines argue that vaccination should be a personal choice.
Others say that growing vaccine scepticism has resulted in pockets of unvaccinated or under-vaccinated individuals who are fertile ground for infection.
The Texas Department of State Health Services on Friday reported 59 new measles cases in three days, taking the state total to 481 since late January.
As of Thursday, the US Centers for Disease Control and Prevention reported a weekly nationwide increase of 124 measles cases, bringing the total to 607.
The nationwide count totalled 285 for all of 2024.
