With the non-exclusive designation, Short can sign an offer sheet with another team. If the Panthers decide not to match, they would receive two first-round picks as compensation.
The Panthers can still sign Short to a long-term contract, but they must do so by July 15 at 4 p.m. ET. If no deal is reached by that point, Short will have to play on the one-year franchise tender.
The deadline for teams to use their franchise tag is Wednesday at 4 p.m.
Short, whose production dropped from a team-high 11 sacks in 2015 to six this past season, said he wanted to remain with the Panthers, even if it meant the franchise tag, which has been estimated at $14,770,194 for a defensive tackle.
"Everybody would like to avoid that,'' Short said of the tag after the season. "If it happens, it happens. If it happens, I'm still going to be professional about the situation.''
The Panthers tried to sign Short, 28, to a long-term deal after he made the Pro Bowl in 2015, but Short was looking for a deal in the range of $17 million per season; Carolina was in the $13 to $15 million range.
Coach Ron Rivera said the former Purdue star was "too important of a player'' for Carolina not to re-sign.
Short, selected in the second-round of the 2013 draft, has 22 career sacks, 179 tackles, 6 forced fumbles and 5 fumble returns.
ESPN's David Newton contributed to this report.