The fan was ejected from the stadium and arrested in the latest in a string of racist incidents involving high-profile players in recent weeks.
The Metropolitan Police confirmed to Britain’s Press Association that the male was arrested and taken to a north London police station on suspicion of an aggravated public order offence.
However, following enquiries, he was released with no further action.
UEFA was informed of the incident through its matchday delegate.
Sterling, who has been an outspoken campaigner in the fight against racism, was the subject of discriminatory language during the first half of the match.
“We can confirm that an individual, who was seated in the away section of the stadium, was ejected and subsequently arrested for discriminatory abuse during the England v Bulgaria match,” said a spokesperson for the FA.
“Wembley Stadium operates a zero tolerance policy on anti-social and discriminatory behaviour and anyone found guilty will be ejected and reported to the police.”
A Chelsea fan was banned for life from attending matches at Stamford Bridge for racist abuse aimed at Sterling in December last year.
Belgium and Inter Milan striker Romelu Lukaku was subjected to monkey chants while playing for Inter Milan at Cagliari earlier this month, while Manchester United’s Marcus Rashford and Paul Pogba are among those to be sent racist abuse on social media after missing penalties for the Red Devils.
Speaking on the eve of the Bulgaria match, Rashford said he believed racism was becoming an increasing problem in football.
“It seems to me like things have been going backwards rather than forwards,” said Rashford.
“To be honest, I’ve always said that the more we speak about it, it doesn’t have much of an impact.
“We’ve tried. There’s been examples everywhere where people have spoken out and I wouldn’t say they’ve been ignored, but nothing has really changed.”