Michael Barrett entered the plea Monday in U.S. District Court in Los Angeles. The 48-year-old Barrett remains free after posting a $100,000 bond on Friday.
U.S. Magistrate Judge Carolyn Turchin set the amount after Andrews' attorney called Barrett's alleged behavior calculated, cunning and secretive and said he posed a threat to the public.
Prosecutors say Barrett found three hotels where Andrews was staying, rented an adjacent room, altered the peephole and shot videos.
Barrett's attorney has said his client has no criminal record and has deep regret for the circumstances that prompted the charges.