Adams, 39, made just three first-class appearances for Hampshire after joining on a short-term contract in September.
Capped once at Test level, the former Essex and Nottinghamshire overseas player also featured in 42 one-dayers.
"There's a lot of scar tissue there and a really high chance of reoccurrence," he told BBC Radio Solent.
"For someone who didn't expect to play first-team cricket for his club, I've done OK.
"It's a nice time to retire. I'm still able to walk and that's important at the end of your career when you've got a family.
"I got a calf tear a week ago and we wanted to see what it looked like on the scan. It's in an area which means I can no longer play basically.
"No matter how fit and strong I get, it's one of those things where it will always be a problem."
Adams's intention was to play for three months at Hampshire before taking up a coaching role in Auckland.
But he admitted his disappointment at not being able to make more appearances for the county alongside a "promising" squad.
"I came here to play and I've had a really enjoyable time doing so," he added. "It's a fantastic county with some great guys and a huge amount of talent."
Adams helped Nottinghamshire to win the County Championship in 2010 and retires with 692 first-class wickets at an average of 23.95.
Hampshire and former New Zealand all-rounder Andre Adams says the risk of persistent calf injuries have forced his decision to retire.