The body was discovered Sunday by officers checking on the woman's welfare, police said. A relative had become concerned.
Daniel Shoffner, 47, was taken into custody on suspicion of murder, police said. A neighbor said he had been living in the home for several months, moving in with the woman after her husband died.
The woman, whose identity had not yet been released, was described as being in her 70s.
The LaPorte County Coroner's Office planned to conduct an autopsy once the body was thawed. Officials said the woman appeared to have been dead for some time, but the cause had not yet been determined.