The hearing dates are scheduled in January and take place in February. Clubs and players are free to negotiate a deal until the arbitrator makes a ruling.
The D-backs have not gone to an arbitration hearing with a player since Damian Miller in 2001.
Arizona would like to bring back Hudson, who made $518,500 last season. The factor leading to his becoming a free agent was the raise he would have gotten through the salary-arbitration process.
Hudson made just nine starts in 2012 before having Tommy John surgery, then in June, just weeks before he was set to return, he reinjured his right elbow during a Minor League rehab start and had to have a second ligament replacement surgery.
The team faced a similar situation with reliever Matt Reynolds, who injured his elbow in June and had Tommy John surgery in September. Reynolds is expected to miss most, if not all, of the 2014 season, and he was eligible for salary arbitration before the sides agreed on a one-year $550,000 contract for 2014 with a $600,000 club option for 2015 in October.
It is believed the D-backs wanted to do something similar with Hudson, but no deal was made before the deadline.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.