I have heard it, almost exclusively from blacks or very rural Southerners.
In the past few years I have been hearing it used that way. I live in Kentucky and I have only heard it from black people.
I first heard it in 2008, from Army folks while deployed. Since then, I’ve heard it many times, always from military people (to be fair, that’s who I spend most of my time around). Anyway, that usage seems to be fairly well used in the military.
That’s the opposite of what Ogre is asking about, I think. In your example “some minutes” is used to mean a noticeable delay, but not literally several minutes. The OP is about “a minute” being used to mean a time period that is really much longer than one minute. The first is emphasis by exaggeration, the second is emphasis by understatement. The latter is more Southern, unless somebody is trying to be funny.
Anyway, certainly I’m familiar with the usage. Distinctions between Southern and black are often pretty fuzzy.
I’m in Newark, NJ and I encounter it only with black patients, most likely older, most likely female. Never heard it before moving here. It makes taking an accurate history a total pain.
“Ma’am, how long have you been having trouble breathing?”
“For a good minute now.”
When I finally nail them down on the time course a minute can mean anything from a couple of days to a couple of years.
Never heard this usage. I’m a white girl from California.
I heard it about an hour ago, in Indiana, to refer to a time period of six years.
seems to be a relatively new thing for the hip hop culture
Data point: the earliest entry for “a minute” (that conforms exactly to the definition I’m using) on Urban Dictionary was from 2002, so it’s been around for a minute. 
I’ve heard it, but only from black folks, and only recently.
Such as:
“I haven’t been to Chicago in a minute.”
Very weird phrasing.
mmm
Just to add to the current discussion…the friend mentioned above is very white and very not-into-hanging-with-black-people if you know what I mean. So he didn’t pick it up from black friends or black family.
Now I’m super curious as to where he got it. Too bad we totally had a fight last month and no longer speak to each other. lol
I don’t think I’ve ever heard the first example, but I use the second one all the time, usually when I’m frustrated with a person who wants something too quickly. “Calm down, it’ll be a minute.” I’m firmly midwestern, a pasty white woman who grew up in a small town with exactly zero black people.
It never struck me as strange before, but I use also “minute” to indicate a short period of time, like most people do. “I’ll be a minute” can mean either a short time or a long time–I guess it’s in the inflection. I’m not sure I’ve heard anyone else use the term since I’ve lived in Chicago, regardless of ethnicity. I’ll have to pay attention, but it might be another one of those things that brand me as not-from-here.
From LA, no family from the South, and I hear this all the time. This is a black thing? Interesting.
I’ve heard it a couple of times (born and raised in Baltimore, MD suburb; currently residing in north-central WV). The only time I ever use it in that context is if, for instance, my hubby would call and ask me to research something for him, and I might reply with something like “Sure, but it’ll take a minute”, meaning, of course, he has to be patient.