The 18-year-old student is believed to be the first person in the UK to appear in a competitive horse race while wearing a hijab.
The amateur rider from Peckham, in south London, won the five-and-a-half-furlong charity race aboard Charlie Fellowes-trained 25-1 outsider Haverland, beating the likes of Olympic cycling champion turned jockey Victoria Pendleton.
“There are no words to describe this – I’m lost for words,” Mellah said.
“When I passed the post I couldn’t believe it, and then I saw all my family and friends and started crying. I am quite competitive, so I wanted to win this race, but I never expected to.
“Horses bring me immeasurable amounts of happiness. I’ve always loved them and always will and I hope to carry on and keep riding.”
BBC presenter Alexis Green, former Apprentice star Luisa Zissman and TV personality Vogue Williams also took part in the all-female race.
Jockey Frankie Dettori told BBC Sport: “I watched the race. It’s incredible, unbelievable. I met her yesterday and she is such a sweet person.”
Mellah learned to ride at the Ebony Horse Club charity in Brixton – but sat on a racehorse for the first time in April this year.
According to the Muslim Women’s Sport Foundation, the number of female British Muslim jockeys – past and present – is in “single digits”.