The incident happened in Charing Cross Road just after 12am today (February 1).
Officers and London Ambulance Service crews attended but found the victim already made his way to the hospital.
He continues to receive treatment for injuries that are not believed to be life-threatening.
A 43-year-old man has been arrested in connection with the investigation and police enquiries continue.
An exit to Tottenham Court Station remained closed until around 7.30am as police dealt with the incident.
TfL warned customers that Exit 4 had been closed due to a police investigation outside the station.
A spokesperson for Metropolitan Police said: “Police were called by the London Ambulance Service at 00:07hrs on Thursday, 1 February to reports of a man stabbed on Charing Cross Road, WC2.
“Officers attended but the victim had already made his way to hospital.
“He continues to receive treatment for injuries that are not believed to be life-threatening.
“It is believed the victim was assaulted in the vicinity of Denmark Street.
“A 43-year-old man has been arrested in connection with the investigation and enquiries continue.
“Anyone with information is asked to call police via 101 quoting reference CAD 38/01Feb.”