Anna Schulz's body was discovered in her Merrillville home on Wednesday night. Schulz taught special education at Lew Wallace High School in Gary.
Police said they arrested the suspect Thursday. His name is not being released.
It appears Schultz's murder may have been the result of a suspect trying to cover the tracks following an earlier crime.
Police say officers were pursuing the teenage suspect for an earlier burglary. During that pursuit on Wednesday he ended up at Schulz's house in the 2500-block of West 58th Place in Merrillville. Police don't believe that the suspect knew Schulz.
Schulz's neck had been cut with some type of edged weapon. Her 2003 silver Cadillac had been taken from the driveway and police later recovered the vehicle in an alley near a home of the suspect's relative.
Police say the 16-year-old suspect was already known to police. They were able to track and apprehend him after contacting his friends and relatives.
"We started connecting the dots when we were in the process of assessing and processing the crime scene. It is when one of the patrol supervisors came up and said that they had tracked him or lost him basically in that same area," said Lt. Jeff Snemis, Merrillville Police Department.
"She was a beautiful, beautiful, striking woman and she was always kind to me," said Denise Brennan, victim's neighbor.
Schulz had been a teacher in Gary for nearly three decades. It does not appear that the suspect knew Schulz.