Carla Stefaniak has not been heard from since 28 November after she went to Central American country's capital San Jose to celebrate her birthday, along with her sister-in-law April Burton.
Ms Burton returned to the US the day before Ms Stefaniak, who dropped her to the airport on 27 November.
After doing some sightseeing the 36-year-old returned to her Airbnb and messaged Ms Burton to say the power was going out in the property. She added that the area she was staying in was unsafe.
Ms Stefaniak had a flight booked for 28 November and had checked in and scheduled an Uber.
She did not however board the flight but the owner of the Airbnb property said he saw Ms Stefaniak get into an unknown car with her luggage at 5am.
"None of us really believe this 5am story because it really doesn't make sense," Ms Burton told Fox News. "There's no reason for her not to contact anyone."
Authorities in Costa Rica said that tracker dogs had found the body partially buried in plastic bags, NBC News reported.
However, there has been no official announcement of the identity of the person who has been found.