They had been expected to attend a basketball game at Southwestern Community College basketball game in Danville, Illinois, on Thursday, according to the post.
In an email to BuzzFeed News, a US State Department spokesperson confirmed the deaths.
"We extend our sincere condolences to friends and family," the spokesperson said. "Our Consulate in Merida is providing consular services. Out of respect for the family during this difficult time, we have no further comment."
Relatives told ABC News that the bodies of the family will be returned to Iowa Wednesday.
In a phone interview with ABC News, Amy Sharp's sister Renee Hoyt said, "My mother is holding up, doing the best she can. We're all supporting her."
Hoyt said knowing the cause of death was not violent gave the family some closure.
"Our main concern right now is getting our family back," she said. "We haven't even thought of any lawsuit or anything like that."