Puello, 24, was placed on waivers last week and cleared. He had been removed from the 40-man roster and outrighted to Triple-A Las Vegas.
However, after being outrighted to Triple-A, Puello informed the Mets that he was hurt, forcing them to rescind the demotion.
According to reporter Adam Rubin, the Mets had to return Puello to the 40-man roster since injuries to 40-man roster players during the last 15 days of spring training entitle that player to be on the major league disabled list while receiving major league service time (April 6).
To make room for Puello on the 40-man roster, the Mets placed Josh Edgin on the 60-day disabled list.
Once Puello is healthy, the Mets will have to again put him through waivers in order to send him to Triple-A.