The sportswear giant took over from previous Manchester United shirt maker Umbro in 2002, and the deal was understood to be worth £24m a year. The forthcoming 2014/15 season will be its last with the club.
Arch rival Adidas is expected to vie with American firm Warrior, which makes Liverpool FC’s kits, to replace Nike, although it has been reported the club is seeking a £60m-a-year commitment from brands.
Nike said in a statement that, although the deal had proved "mutually beneficial" over the past 12 years, the Premier League club was demanding too much money to renew the agreement.
The statement read: "Manchester United is a great club with passionate fans. We are proud to have partnered with them for the last 12 years and will continue to sponsor the club until the end of the 2014/15 season.
"Any partnership with a club or federation has to be mutually beneficial, and the terms that were on offer for a renewed contract did not represent good value for Nike's shareholders. We look forward to a successful final season with the club."
It comes the day after Manchester United revealed its latest kit, the first to feature new sponsor Chevrolet on its shirts.
Chevrolet has launched the record-breaking sponsorship deal, worth an approximate £350m over seven years, with a global campaign asking fans "What Do You #PlayFor?"