Barry and Carol Bennett, both 63, were found by a friend who performed a welfare check after phoning the Todd County Sheriff's Office to report that they had not responded to texts or phone calls since Tuesday.
In court documents filed Friday, authorities said the Bennetts died of "multiple gunshot wounds" at their home in Long Prairie, a town of about 3,500 about 100 miles northwest of Minneapolis. An arrest warrant has been issued for the couple's son, Dylan Bennett, who is charged with two counts of second-degree murder.
Authorities believe the Bennetts were killed Monday, the day Barry Bennett was last seen alive.
Dylan Bennett's car was found at the home, with an empty box for a 9mm handgun and a box for ammunition inside. Carol Bennett's car was missing.
According to the criminal complaint, Barry Bennett told the Todd County Sheriff's Office in December that Dylan had expressed thoughts about killing his parents while he was in a mental health treatment facility.
The criminal complaint outlines how authorities tracked Dylan Bennett's movements in recent days.
On Monday morning, Dylan Bennett was seen driving his car during a bank transaction in which a large sum of cash was withdrawn from the Bennetts' account, the complaint said.
Carol Bennett's credit and debit cards were used in Wisconsin, Illinois and Ohio on Monday, Tuesday and Wednesday. Her car was found in Columbus, Ohio; Dylan Bennett had a plane ticket for a flight from Columbus to Cancun, Mexico.
Authorities believe Dylan Bennett was in Mexico on Thursday, based on phone usage.
He subsequently became a physical education teacher in Long Prairie but later retired from that job, according to The Star Tribune.
“It hit hard this morning,” said Jon Kringen, superintendent for the Long Prairie Grey Eagle School District. “Everyone was in shock when they heard. It’s impossible to comprehend that this could happen. People are lost for understanding. … He and his wife were good people.”
The Minnesota Bureau of Criminal Apprehension and the Central Minnesota Violent Offender’s Task Force are assisting in the investigation.
Fox News' Melissa Leon and The Associated Press contributed to this report.