The 26-year-old right-hander recorded five saves during the Mets' memorable postseason run, but he blew three opportunities in the World Series.
Familia signed with the Mets as an amateur in 2007 and has been with the organization ever since. He made his debut in 2012 and has a career 2.42 ERA over 169 appearances.
William Boor is a reporter for MLB.com. Follow him on Twitter at @wboor. This story was not subject to the approval of Major League Baseball or its clubs.