Parrish, 25, joined the Shrimps from Bury in 2008 and, having already made over 200 appearances, will now remain until the summer of 2016.
Manager Jim Bentley told the club's official website: "It's great news for everyone. Andy is a fantastic professional and a firm fans' favourite.
"He is a big member of our squad and is a virtual ever-present. He can play anywhere along the backline and is vital to what we want to achieve here.
"I am delighted he has signed up again because he is the perfect age and still getting better and better."
- Sports & Recreation