Lowe move to stadium:mk last summer and, after a slow start to life in Milton Keynes, ended the campaign as joint-top scorer with 12 goals alongside Dean Bowditch.
Explaining the reasons for opting against another season under Karl Robinson, the 34-year-old told MK Dons' official website: "This wasn't an easy decision but it was one I felt I had to make for the benefit of my family.
"Constantly being away from my young family in Liverpool last season proved more challenging than I originally thought and I found it hard to concentrate fully on my football.
"I had a long think over the summer and after speaking with my family and Karl, I felt it would be for the best if I left.
"I really enjoyed my short, but memorable time in Milton Keynes and I wish the boys every success next season."
Boss Robinson added: "A motivated Ryan Lowe is a top forward in this league but for the reasons he stated to me earlier this week, I didn't think he'd be in the right mindset to help take this club forward.
"I'd like to wish him luck in the future and thank him for all he did last season."