Attorney general Jeff Sessions said that the FBI's Richmond field office and Rick Mountcastle, the US Attorney for the Western District of Virginia, would lead the investigation.
Cruz called the violent clashes surrounding white nationalists and counter-protesters "acts of domestic terrorism".
The "Unite the Right" rally included white nationalist and other far-right groups protesting Charlottesville's plan to remove relics of its Confederate past, such as a statue of Confederate Gen. Robert E. Lee.
The president's silence had been noticeable Friday night, as a few hundred tiki torch-bearing white supremacists - mostly young men - paraded through the University of Virginia campus while chanting racist taunts and flaunting Nazi paraphernalia.
A 32-year-old women died when a vehicle plowed into a crowd dispersing after police broke up the melee in the city's downtown. He said they are not white supremacists and are only interested in free speech.
First Lady Melania Trump called for peace after the violence erupted Saturday.
"You came here today to hurt people and you did hurt people, but my message is clear - we are stronger than you".
"This represents a turning point for the people of this country", former Ku Klux Klan leader David Duke spoke at the rally, "We are determined to take our country back".