The 27-year-old Murphy hit .291 with six homers and 65 RBIs last year, when he made $512,196. The second baseman had asked for $3.4 million in arbitration and had been offered $2.55 million.
The club last went to an arbitration hearing in 2008, with Oliver Perez and Scott Boras.
Free-agent pitcher Shaun Marcum took a physical Tuesday and the Mets hope to finalize his agreement on Wednesday.
The team also signed reliever Scott Atchison to a minor league contract with an invitation to spring training. The 36-year-old right-hander was 2-1 with a career-best 1.58 ERA in 42 games for Boston last season.
ESPNNewYork.com's Adam Rubin and The Associated Press contributed to this report.