Nidal Hasan, who shot dead 13 unarmed US soldiers at Fort Hood army base in 2009, is expected to be executed on 3 December.
"People need to understand that there's [sic] serious consequences for these types of things," said Hegseth.
The decision to livestream it is "unprecedented in the modern era" and "on uncertain legal terrain," said John Mills, a lawyer who works with inmates sentenced to death.