White was part of Ireland's World Cup squad last year, and went on to make 13 appearances for the national team in 2015 and 2016 after qualifying on residency grounds.
"While it's disappointing to finish up this way and not on my own terms, I feel that I can look back at my rugby career with a lot of pride," White said in a statement.
"I am retiring at 35 years of age, and with so many great memories from my time playing in both New Zealand and Ireland. I am not sure what exactly the future holds, but I know I am really excited about it. I've loved my time as a player, but feel I am ready to move on now and challenge myself in other ways."
Connacht chief executive Willie Ruane added: "Nathan has been a very important part of the team and organisation over the last number of years.
"He has contributed a great deal to the culture here and has inspired so many young players with his leadership on and off the pitch. He will, of course, be sorely missed at Connacht Rugby, but he can be proud of what he has achieved both here and with Ireland."
White's concussion problems stem from a match against former club Leinster in March of this year.