Coach Justin Fuente announced the indefinite suspensions Tuesday.
The online database for Montgomery County General District Court states that Alexander, a sophomore, and Gaines, a redshirt freshman, were both arrested April 24 for marijuana possession. Gaines also was charged with possession of alcohol.
All the charges are misdemeanors.
Alexander was penciled in as one of the Hokies' starting cornerbacks. Gaines stood out with two sacks in Virginia Tech's spring game on April 23.
In a release, the school said Fuente would have no further comment about the suspensions.