The team said Tuesday he died last week of complications from pneumonia following surgery.
"I was sorry to learn about the passing of Barry Hill," Dolphins vice president/special adviser Nat Moore said in a statement. "Once again the Dolphin family has lost one of its own far too early. On behalf of the entire Miami Dolphins organization I want to pass along our condolences to his family."
Hill set Big Eight Conference records at Iowa State for career interceptions (21) and interceptions in a season (nine). He also played basketball for the Cyclones before being drafted by the Dolphins in the fifth round in 1975.
He appeared in 20 games during his two seasons with Miami and blocked a field-goal attempt on the final play of the 1975 preseason to preserve a 14-13 victory over the Denver Broncos.
His funeral is Saturday.
The Associated Press contributed to this report.