A 19-year-old man, who is a Norwegian national of Somali origin, was arrested on suspicion of murder, after a Taser was used to detain him.
Police said mental health was a "significant factor" in the incident.
He was taken to hospital for treatment and is now in police custody in a south London police station.
Mark Rowley, the Metropolitan Police’s assistant commissioner for specialist operations, said the investigation is being led by the force's homicide command unit, with support from the counter-terrorism unit.
A spokesperson for the Community Security Trust said CST had been in close contact with police since very early this morning, regarding the “possible terror stabbing in Russell Square".
