The 29-year-old struggled at the beginning of the 2013 season, but he finished strong. From 2011-12, Hernandez was one of the league's better setup men.
"If he is healthy, he's going to be really big for us," general manager Dave Stewart said. "Hopefully, we can keep him healthy, keep him going this year, because he would be big for us."
Hernandez had Tommy John surgery last April and the team is planning on being conservative with his rehabilitation so it seems unlikely that he will be ready for Opening Day. May seems to be a more realistic target at this point.
Hernandez was acquired by the D-backs in December 2010 from the Orioles in a trade that sent Mark Reynolds to Baltimore.
The move leaves the D-backs with four players eligible for salary arbitration: Jeremy Hellickson, Cliff Pennington, Addison Reed and Mark Trumbo.
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.