The Championship club have banned the teenager for "the foreseeable future" following an investigation by both clubs and the FA after the Trotters forward reported the incident
The ban follows an investigation by both clubs and the Football Association after Sordell reported he was abused while warming up as a substitute, revealing other team-mates also suffered abuse on the day.
The fan will not face a life ban from Millwall due to his age, but will in fact be offered a place on the 'Millwall for All' educational program as the club "hope we can change his outlook on equality, racism and life in general."
Sordell responded to the abuse on 6 October, Tweeting: "Putting the match aside, its 2012 in england and people are still shouting racial abuse at a football game!? #Shocking."
Sordell stated Lee Chung-Yong, Darren Pratley and Benik Afobe were also abused at the game, with nearby police doing little to combat the racist taunts.
He continued: "Chungy, Pratts, Benik and I had all sorts of things said to us. The police were standing yards away and did nothing ..."
Millwall stated they have a "duty" to rehabilitate the 13-year-old, saying: "The individual has been banned from Millwall matches for the foreseeable future, but as a club we also felt, given the boy's age and background, we had a duty to play our part in attempting to educate and rehabilitate him."
The club also confirmed the fan wrote a letter of apology to Sordell, which the player has accepted. The FA commended the approach of both clubs during the investigation, as well as that of Sordell and the PFA.