Police say there were two separate shooting incidents - one at West Ambler Johnston Hall, a student dormitory, and Norris Hall, an engineering building.
The incidents were about two hours apart. Police say they believe there was one gunman and that he is dead.
The state university in the town of Blacksburg is home to 26,000 students.
"We have a ballpark figure on fatalities. It's at least 20 fatalities," Virginia Tech police chief Wendell Flinchum said.
