Warning: Story contains coarse language
Jones recorded a video in which he showed off the package containing the jerseys - before burning them one by one in his driveway.
"I'm not the one to f--- with Joe Haden," Jones wrote in the post caption.
"I opened up my mailbox today and I had these jerseys in my mailbox," Jones said. "I don't know what f--- you all have going on. ... I'm going to show you how (gangster) I am ... All these b------ are about to get fired up."
Haden, for his part, denied any involvement.
"I didn't send you those jerseys. Why would I ever do that?" he wrote to Jones. He also recorded a video saying he doesn't know how the jerseys ended up at Jones' home.
Jones, who also stood out as a return specialist throughout his career, played for four different NFL clubs from 2005-18, authoring his longest single-team tenure with the Bengals from 2010-17. The 36-year-old played against the Steelers - Cincinnati's AFC North rivals - 12 times.
Jones also faced Haden on several occasions; Haden was a member of the Cleveland Browns from 2010-16 before joining Pittsburgh in 2017.