The move marks the first time a governor has asked for genetic testing of someone already put to death.
The testing comes in the case of Roger Keith Coleman, a convicted killer whose proclamations of innocence sparked concern nationwide over whether the wrong man died in Virginia's electric chair.
"We have found that the latest DNA technology -- in certain instances where the other facts of a case support it -- has provided a definitive result not available at the time of trial or post-conviction testing," Warner said in a statement.
Coleman was convicted and sentenced to death for the 1981 brutal rape and stabbing of his sister-in-law, 19-year-old Wanda McCoy.
The tests, on vials of evidence that have been preserved for years at a California laboratory, are being conducted at the Center of Forensic Sciences lab in Toronto, Ontario. Results could be announced before Warner leaves office next week.