The 27-year-old won the title for his career performance against the Indianapolis Colts last week. Greene accumulated 161 yards on the ground in 32 rushing attempts, while finding the end zone three times in New York's 35-9 victory.
Greene's 32 carries surpassed his previous career high of 27 while his 161 rushing yards were 17 more than his previous career best. The three touchdowns tied a career high for Greene.
The FedEx Ground Player of the Week is an award decided by fan votes. Greene's career game gave him the edge over several other running backs for the award, including a pair of running backs that reside in the same state in Ahmad Bradshaw of the New York Giants and C.J. Spiller of the Buffalo Bills.