The arrest followed YouTube footage which appeared to show signs promoting Magpies' owner Mike Ashley's Sports Direct brand being damaged on 8 March.
The teenager was also questioned over damage to a Sports Direct store in the city on the same day.
A Northumbria Police spokesman said: "Officers are investigating two incidents of criminal damage, one at the Newcastle ground and the other at the Sports Direct store on Blackett Bridge in Newcastle on 8 March.
"A 16-year-old male was arrested on suspicion of criminal damage and has been bailed pending further inquiries.
"Detectives are continuing to examine CCTV footage and photographs of the incident which have been circulated via social media."