Moore, who missed nearly all of the 2011 season because of a torn medial meniscus in his right knee, was hurt during Tuesday's spring training game against Cincinnati while trying to block a ball. He finished the contest and went 2-for-2 with a pair of runs batted in and iced the wrist afterward.
Pain persisted in the wrist Wednesday and an x-ray revealed the fracture. He is expected to visit a specialist and will have his hand placed in a cast.
Moore was 4-for-6 in three games this spring. He played just two games last year, suffering his knee injury in an April 7 game against Texas.
In 68 games over parts of three major league seasons, all with Seattle, the 27-year-old Moore is a .197 hitter with five homers and 17 runs batted in.