Malvo, who pleaded guilty to six murders, is serving six consecutive life sentences without parole.
Jonathan Sheldon, Muhammad's lawyer, had argued that Virginia would be executing a man with severe mental illness and that his sentence should have been commuted to life imprisonment, but the US Supreme Court turned down Muhammad's appeal on Monday.
Some family members of those killed during the sniper attacks had said they would watch Muhammad's execution.
Cheryll Witz, whose father John Taylor was shot dead on a golf course in an attack that Malvo confessed to carrying out at Muhammad's direction, said: "[Muhammad] basically watched my dad breathe his last breath … Why shouldn't I watch his last breath?"
But Beth Panilaitis, executive director of Virginians for Alternatives to the Death Penalty, had argued that life imprisonment would still have ensured the safety of people living in Virginia.
"The greater metro area and the citizens of Virginia have been safe from this crime for seven years," Panilaitis said.
"Incarceration has worked and life without the possibility of parole has and will continue to keep the people of Virginia safe."
The sniper attacks terrorised the Washington region, with victims shot while carrying out chores like shopping or filing their cars at fuel stations.
"It was such a frightening time that people would not go outside - they would not eat outside or go to meet their friends," Rosiland Jordan, Al Jazeera's correspondent in Washington DC, said.
"Children were locked inside. I covered a practice field on a Saturday inside a military base where there were 60 football games taking place because parents did not feel secure enough to go to a local public park or a school field to have their children burn off some of that excess energy."
Police captured Muhammad and Malvo on October 24, 2002, as they slept in their car at a Maryland lay-by.
The car was found to have been modified so that a sniper could hide in the boot and fire his weapon through a hole drilled through the bodywork.