Gruver was taken to a Baton Rouge hospital for what school officials are calling a medical emergency.
Alexander expressed condolences to Gruver's family at a press conference Thursday.
LSU officials say they are aware of the incident and are working on a statement.
The cause of death has not yet been confirmed, but an autopsy will be conducted on Friday, according to the coroner's office. All Greek activities are shut down on LSU's campus until further notice. That means no Greek organized social activities or pledging, he said.
Alexander added that Phi Delta Theta has been suspended by LSU and its national chapter.
The Phi Delta Theta General Headquarters also is investigating the incident and the fraternity, and has suspended the frat's operations while the investigation is underway. Gruver was an LSU student from Georgia.
"The death of Maxwell Gruver was tragic and untimely", Alexander said.
"LSU officials are aware of an incident that occurred last night involving a fraternity, LSU is now investigating and will report as soon as more information is available". "LSU is now investigating and will report as soon as more information is available".
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