Christina Edkins was killed in Hagley Road, Birmingham, during the morning rush-hour on Thursday.
A spokesman for West Midlands Police said the man will now be sent to a secure facility, after the latest assessment by mental health professionals deemed him unfit to be interviewed any further by detectives.
Police said the suspect had been regularly assessed by medical experts throughout his time in police custody. He was arrested near the scene of the attack on Thursday.
Christina had been sitting in front of her attacker on the top deck of a double-decker bus when he struck as the vehicle was slowing down.
Post-mortem tests have revealed the teenager died from a single stab wound to the chest.
Detective Superintendent Richard Baker said after the attack: “He walked down the stairs and calmly waited to get off the bus.”
Yesterday, friends of the teenager gathered to pay their respects at the scene, where a growing number of floral tributes have been placed.
Police have released a picture of the suspected killer, a black man in his early 20s, who was wearing a distinctive jacket with a picture of a tiger on the back and have appealed for anyone who saw him between 6am and 1pm to come forward.