Hnidy, 34, has played 547 games for six NHL teams, including the Minnesota Wild in 2009-10. He has notched 16 goals and 55 assists, and his NHL plus/minus ratio is plus-16.
Hnidy will report to training camp with the rest of the veterans on Sept. 18.
Earlier this week, the Coyotes extended a similar training camp tryout invitation to free-agent center Kyle Wellwood.
Reach Dave Vest at firstname.lastname@example.org and follow him on twitter @davest4yotes.