TL;DR: If like the comics, there is an entire mountain range full of Vibranium in Africa.
Although we have yet to see where Vibranium comes from in the MCU, Howard Stark described it as "the rarest metal on earth". Here is the dialogue from Captain America: The First Avenger:
STEVE: What about this one?
HOWARD: No, no that's just a prototype.
STEVE: What's it made of?
HOWARD: Vibranium. It's stronger than steel, and a third of the
weight. It's completely vibration absorbent.
STEVE: How come it's not standard issue?
HOWARD: That's the rarest metal on Earth. What you're holding there -
That's all we got.
However, if they stick to the comics origin for Vibranium, it can only be found in the African nation of Wakanda. In both the 616 and Ultimate continuities, pure Vibranium is mined from the central mountain range of Wakanda, which in actuality is a gigantic meteor that landed on the Earth millions of years ago... perhaps even the one that killed the dinosaurs.
The Wakandan mountains are the central feature of the tiny nation, and the Wakandan capital - usually referred to as Wakanda City - is built within the center of the mountains. Given the near-indestructible nature of the Vibranium within the mountains, this has allowed Wakanda to survive numerous conquest attempts by its many neighbors and/or outside forces.
Furthermore, the Wakandans have built their culture around the mining & use of Vibranium, allowing their primitive nation to flourish into one of the most technologically advanced places on Earth. Those few invading armies that made it past the mountains have found an army equipped with Vibranium-tipped spears & arrows, buildings made of Vibranium-laced stone, and a king wearing Vibranium mesh armor.
Within the comics continuity, Ulysses Klaw is one of the few individuals who managed to infiltrate Wakanda and steal Vibranium. Although he was caught & branded on at least on attempt, this has made him a fortune selling the metal on the black market. He is considered to be one of the world's foremost experts on Vibranium, and one of the only sources outside of Wakanda itself.
In Avengers: Age of Ultron, Ultron pays a visit to
a mining operation in Africa, which is being run by Klaw (Klau in the MCU). Klaw shows Ultron his hidden cache of Vibranium, which Ultron purchases for several billion dollars (right before losing his temper and cutting off Klaw's arm). Where Ultron got the money is anyone's guess, but he likely either stole it from bank accounts around the world, or simply told the bank's computers that Klaw's account had that much in it (with no actual money moving around). Either way, the result is the same.
This scene would seem to confirm that the MCU version of Vibranium is very similar, if not identical, to its comic counterpart. Given that the Wakandan government is extremely hesitant to export Vibranium, it's not difficult to assume that Captain America's shield represents all of the metal the US government has managed to acquire at the time.