Garner said two of the three people injured in the shooting remained in critical condition while a third was in stable condition.
Local television WAFF, citing local authorities, said the shooter was a female staff member who had opened fire after learning at a biology faculty meeting that she would not be granted tenure.
The television station said all three fatalities were staff members at the university.
The local Huntsville Times reported that a female biology professor had been taken into custody and that her husband had been detained.
Erin Johnson, a second-year student, told the newspaper that a biology faculty meeting was underway at the Shelby Center when she heard screams coming from one of the rooms.
History of shootings
The incident was the latest in a series of school shootings to rock the United States, most of which have been carried out by students, amid the nation's ever-prevalent debate about gun control.
The shooting comes more than two years after the southern state of Virginia was left horrified by the April 2007 massacre of 32 people at the Virginia Tech university by a student gunman, Seung-Hui Cho, who turned his gun on himself.
In 1999, two teenagers went on the rampage at Columbine school, Colorado, gunning down 13 people before killing themselves.
In the first six weeks of this year alone several shootings have already been reported around the country.
Last month, eight people were killed in the southern state of Virginia. A man surrendered to authorities after a massive manhunt in the woods near the historic town of Appomattox, during which he opened fire at a helicopter aiding the search.
And in early January a disgruntled employee at a Missouri plant of a Swiss power company went on the rampage shooting dead three people and wounding five others.
He also killed himself in the bloody shooting, believed to have been triggered by a dispute with the ABB company over his pension funds.