She's the first female board member of the Saudi Arabian Motor Federation, and serves as the Saudi Arabian representative at Women in Motorsport Commission for FIA.
Asked whether there would now be female Saudi racing drivers, she replied: "For sure, definitely".
Saudi Arabia was the only country in the world where women were banned from driving.
Saudi Arabia is among the most conservative countries in the world and women have traditionally had much fewer rights than men.
Some still face resistance from conservative relatives, and many accustomed to private drivers say they are reluctant to take on the country's busy highways.
Human Rights Watch last week said the kingdom has arrested two more female activists and many others have been barred from travelling outside the kingdom, in what it denounced as an "unrelenting crackdown".
Official statistics show that women make up the overwhelming majority of job seekers in Saudi Arabia and that around 34 percent of Saudis seeking employment are between 25 and 29 years old.More news: First Signs Of Strain Show Between English Team And Their Media
Prince Mohammed, appointed heir to the most powerful throne in the Middle East a year ago this month, has also lifted a ban on cinemas and mixed-gender concerts, following his public vow to return the kingdom to moderate Islam.
Michele Mouton, a former rally driver and president of the FIA's commission, said in a statement she hoped Ms Al-Hamad's example would help pave the way for more Saudi women to get involved.
"It was ideal. Everything was smooth, I felt I belong in the seat", she said afterwards.
Twitter exploded with videos of Saudi women driving for the very first time, highlighting their experiences with the hashtag #saudiwomendriving. There's also a waiting list of several months for a courses in major cities where they are offered.
Others already own cars driven by chauffeurs and are in no rush to drive themselves.
"Worst of all will be if these small-scale reforms, and the silencing of feminists, slow the momentum for pushing the Saudi regime into making more meaningful change", she wrote in a United States newspaper. "It will take me two months to save up enough to pay for the license fee", 20-year-old literature student Salwa al-Zahrat told Reuters, "and then it will take me three years to save up for a auto".
They could detain groups of unmarried men and women for simply standing around or sitting together.
Myself as a man, or any man, when he sees a woman, he'll give her the priority and give her the right of way to drive, and protect her.