Wright was subbing for Josh Lambo, who was placed on injured reserve with a left hip injury. Wright was waived/injured Monday in a corresponding move.
The Jaguars also signed former New York Giants kicker Aldrick Rosas to their practice squad. The Giants released Rosas in July after he was charged with three misdemeanors stemming from a hit-and-run crash in Butte County, California, in June.
The Jaguars also waived defensive tackle Tim Jernigan, whom they signed on Aug. 17 to help shore up a defensive line besieged by injuries. Jernigan played in all three games and had one tackle and one assist.
Hauschka won a Super Bowl with the Seattle Seahawks in 2013 and signed with the Bills four years later, making 87.9% of his kicks in his first season in Buffalo. He made 78.6% of his field goals in each of his past two seasons, however, including just 41.7% of his attempts for 50 yards or longer.
He spent six seasons as Seattle's starting kicker after stints in Baltimore and Denver.
ESPN's Michael DiRocco contributed to this report.