Muhammad is scheduled to be executed Nov. 10 for the October 2002 killing spree that left 10 dead in the nation's capital, Virginia and Maryland.
"I know of nothing in this case now that would suggest that there is any credible claim of innocence or that there was anything procedurally wrong with the prosecution," Kaine said on his monthly call-in radio show on WTOP.
Kaine said he would review Muhammad's petition for clemency when he gets it.
Muhammad attorney Jon Sheldon said there were "huge procedural errors in the case" that he plans to raise in the clemency petition he expects to file in mid-October, and other issues he'll raise in a motion with the U.S. Supreme Court in early November.
Muhammad was sentenced to death for the slaying of Dean Meyers, who was shot at a Manassas gas station. Myers was one of 10 people killed over a three-week period in 2002 by Muhammad and his teenage accomplice Lee Boyd Malvo. Malvo is serving a life sentence.
In August, a three-judge panel of the 4th U.S. Circuit Court of Appeals unanimously rejected Muhammad's claims that prosecutors withheld critical evidence and that Muhammad should not have been allowed to act as his own attorney for part of his trial.
Muhammad made his own opening statement and questioned 18 witnesses before turning his defense over to court-appointed attorneys. During oral arguments in May, Sheldon argued that Muhammad's trial lawyers failed to tell the judge that he was too mentally impaired to represent himself.
Muhammad also claimed prosecutors withheld thousands of pages of documents that could have helped him, including ballistics reports, witness interviews and an FBI profiler's report that the shootings probably were the work of a lone gunman.
Judge Roger Gregory wrote in the opinion that the court did not condone the state's actions, adding that the prosecution should err on the side of disclosure -- especially when the defendant is facing a possible death sentence.
"Yet, at this stage of the criminal process, we deal only with actions that were clear violations of the Constitution. While not admirable, the Commonwealth's actions did not violate the Constitution," Gregory wrote.
Sheldon said death shouldn't be allowed because of fuzziness between the degrees of constitutional violation.
"So not only was it improper, but it apparently was likely a violation of the constitution, just not a 'clear violation,'" he said in an e-mail to The Associated Press. "I'd call that affirming a death sentence on a technicality."
Kaine usually does not act on clemency petitions until after the courts have denied a condemned inmate's request.
Kaine, a Roman Catholic, is opposed to the death penalty, but has allowed nine executions and commuted one sentence since he took office in 2006. Virginia has the nation's second busiest death chamber behind Texas.