Simpson County Sheriff Kenneth Lewis said it appeared Upshaw. 53, died from a gunshot wound to the head that "appeared to be self inflicted," WLOX-TV, Biloxi, Miss., reported.
Other officials would not comment on the details of her death.
Upshaw's body was found Sunday in the home of former state Rep. Clint Rotenberry in Mendenall, Miss.
Mississippi Bureau of Investigations spokesman Warren Strain said a crime scene unit was conducting interviews and following leads.
"It would be premature to make any statement regarding the investigation at this point," Strain said.
"She's passed; that's all I know at this point," Simpson County Coroner Terry Tutor said. "I've given it to MBI. They're doing their investigation on it."
Upshaw, a Republican, served in the Legislature since 2004 and was chairwoman of the Conservation and Natural Resources Committee.
"Deborah and I were saddened to hear of the passing of Rep. Jessica Upshaw," Gov. Phil Bryant said in a statement. "I have known Jessica for many years as an unselfish and dedicated public servant. This is a tragic loss for her family and all Mississippians, and our thoughts and prayers go out to her family during this difficult time."
Republicans and Democrats said they were stunned by Upshaw's death, The Clarion-Ledger reported.
"I am deeply saddened by the passing of my dear colleague Representative Jessica Upshaw," said Rep. Bobby Moak, a Democrat. "Jessica was a fixture in her seat on the back row of the chamber, where she passionately championed causes for her district and the state. This is an instance where replacement is not possible. Jessica will be sorely missed."
House Speaker Philip Gunn said Upshaw was an "outstanding legislator and friend. She was one of the brightest and most competent members of the House. Our hearts break for her family, and our prayers go out to them during this tragic time."
GOP Rep. John Read, a longtime friend, said Upshaw's daughter and son-in-law, working in South Korea, recently brought the legislator's grandson to Mississippi for a visit.
"She was very close with her daughter and with her mother, just loved her family," Read said. "Her heart was just so big. She'd do anything for you. She was just a sweet person. I'm just shaken by this. We have lost a good person."