He survived with only minor injuries.
Cohn, winner of the 1991 Grammy for best newcomer and best known for the song "Walking in Memphis,"
Cohn says he and his entourage were within "two minutes" of their hotel when they spotted a man running really fast toward their van and, "I just said to nobody in particular in the van, 'I wonder who that guy is running from?' And a few seconds later, I found out.
"This guy appeared right in front of the van, had a gun, and within seconds he was pointing it at our van. I yelled, 'Duck!' I heard a shot as I was ducking."
But Cohn says he didn't even realize he'd been hit: "I think the shock of the event prevents you from feeling anything. I did not feel any pain at all."
Since then, Cohn says, his emotions have run the gamut.
"They warned me about this right away, that there'd be some post-traumatic stress," he said. "I've had a lot of feelings. I've cried a lot, I've laughed a lot, I've been sort of edgy sometimes. Mostly, right now, I'm feeling a lot of gratitude for just being here.
"But, clearly, I do have thoughts once in awhile, intermittently, trying to process how close it was. And, so far, I haven't been able to really process it. It's too big."
Cohn is married to ABC News anchor Elizabeth Vargas and has three children, including a 2-year-old son he had with Vargas.
"All I'm feeling right now is grateful that I'm here to talk about it," he says. "And to see my kids and be with my family and my wife and, hopefully, continue to write and record and sing and all these things that, but for another centimeter, I wouldn't have been able to do."
Cohn says he doesn't know the man who shot him but says he's clearly troubled.
"I don't feel anger," he says. "That may come later, you know? I don't know. Right now, I'm just relieved he was caught. He can't hurt anybody else. And that's all I can really tell you about that. It's not where I'm going in my thought process. I'm just not thinking about him at all."