It depends how you think of it.
If your intent is, "an icon that belongs to 1990", then you should write "1990's icon".
If your intent is, "an icon that belongs to the decade of the 1990s", then you should write "1990s' icon".
But we also often use nouns as adjectives without using a possessive. Like, "this is an automobile part". It's not a possessive. The part may belong to an automobile in some sense, but the point isn't to say that it belongs to an automobile, but rather that it is a part and it is of "type" automobile. Similarly for, say, "a baseball bat". We could say, "a baseball player's bat" and make it a possessive, but we're saying is that it is a bat of type baseball. "A computer keyboard", "a hardware store", etc.
So I think it's more common to write "a 1990s icon" in this sense. It is not a possessive, it is not an icon that belongs to the 1990s. Rather, it is an icon of type 1990s.