The spectator, in a letter of complaint to the ECB, also said women were subjected to sexist chants while homophobic abuse was directed at some players by the same group of people.
The England and Wales Cricket Board (ECB) is "extremely disturbed" by allegations of racist chanting as well as sexist and homophobic abuse by spectators during the fourth Ashes Test against Australia at Old Trafford.
British media reported that a supporter had left the ground on the second day of the Test on Thursday after hearing a section of fans singing a racist song about England's Barbados-born fast bowler Jofra Archer.
The spectator, in a letter of complaint to the ECB, also said women were subjected to sexist chants while homophobic abuse was directed at some players by the same group of people.
"The ECB is extremely disturbed to hear that a report was made regarding anti-social behaviour from a group of spectators during the fourth ... Ashes Test match at Emirates Old Trafford," ECB said in a statement released to British media.
"While this is a relatively isolated incident there is absolutely no place for anti-social behaviour within the game and it is vitally important that all spectators feel able to report anti-social behaviour and feel safe in doing so."
The incident comes on the heels of an annual report from British anti-discriminatory body Kick It Out that showed a 43% rise in reports of racist abuse in English football last season.
Manchester City's Raheem Sterling and Manchester United's Marcus Rashford are among those to have spoken out about being subjected to online racist abuse.