If the balloon popped by itself, then:
the balloon popped.
the balloon (has) burst.
If the balloon was actively popped by a person:
Derek popped the balloon.
The balloon was popped.
The balloon has been popped.
The following does not look like common usage, since popped and burst are more often used as verbs than as adjectives:
the balloon is popped *
If you prefer an adjective, then ripped, ruptured, broken. Or maybe a "popped balloon" (an attributive adjective).
What about - A few minutes later? A few days later? A few months later? A few years later?
If it just happened a second ago, then you could say:
The balloon just popped.
The balloon popped.
If it happened a few minutes or hours ago:
The balloon popped.
The balloon was popped.
The balloon has been popped.
If it happened a year ago:
This looks like a popped/broken balloon.