The 18-year-old from Ismailia also became the first Arab woman to be presented with a medal in weightlifting.
Xiang Yanmei won gold, China's fourth in weightlifting at the Rio Games, while Kazakhstan's Zhazira Zhapparkul took silver.
"This is such a big honour," said Ahmed, who won the Youth Olympic Games title two years ago. "All Egypt was waiting for one or two medals from our team."
Technically, Abeer Abdelrahman preceded Ahmed as the first Egyptian woman to land an Olympic medal.
At the 2012 London Games, Abdelrahman finished fifth in the women's 75kg but with the top three athletes later all testing positive for banned substances, she will be elevated to the silver medal.
"But I was the first to be on the podium," smiled Ahmed, who said she took up weightlifting after being introduced to the sport by her brother.
Before the International Weightlifting Federation changed the rules in 2011 to allow Muslim women to wear a full-length unitard, very few females practised the sport in the Arab world as they considered the clothing immodest.
Ahmed, who wore a full-length unitard and a sports hijab while competing, said: "I hope it will encourage other girls to take up the sport. A new weightlifting generation can be born, a new beginning."
Weightlifting and handball were the most popular sports for Egyptian girls, she said, before adding: "I hope I can help to re-establish Egypt as a successful weightlifting nation."
Egyptian men have won nine weightlifting medals, including five golds, but the most recent was claimed in 1948.
Ahmed made six good lifts but endured an anxious wait for her podium finish when Colombia's Leidy Solis Arboleda made her last clean & jerk attempt at 146kg.
The Colombian, who would have edged Ahmed out of the medals with a successful lift, failed and Egypt's coaches celebrated loudly.
Xiang won with a lift to spare, totalling 261kg. Zhapparkul, the youngest of seven sisters, made 259kg.
(Editing by Mark Lamport-Stokes)
