Gudbranson, a 29-year-old defenseman, scored three points (one goal, two assists) in 36 games and can become an unrestricted free agent after this season.
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Selected by the Florida Panthers with the No. 3 pick in the 2010 NHL Draft, Gudbranson has scored 76 points (21 goals, 55 assists) in 554 regular-season games with the Panthers, Vancouver Canucks, Pittsburgh Penguins, Anaheim Ducks and Senators. He has scored one goal in 17 Stanley Cup Playoff games.
The Predators have several defensemen injured, including Mark Borowiecki (upper body), Alexandre Carrier (lower body), Dante Fabbro (upper body) and Luca Sbisa (lower body).
"Erik is a veteran player. He's a big, physical defenseman," Nashville general manager David Poile said. "I think that falls into the theme of the identity that we want our team to play. As we know we've been very banged up all over our lineup but especially on defense, and I think Erik certainly gives us some good depth as we head into the last 13 games of the regular season.
"He will get to Nashville as soon as he clears quarantine and immigration. Hopefully that won't be too long, but it certainly won't be [Tuesday]. Probably later in the week."
Fortunato, a 24-year-old defenseman, has no points in nine games with Cleveland of the American Hockey League. The defenseman can become a restricted free agent after this season.
The Predators (26-12-4) are fourth in the eight-team Discover Central Division, four points ahead of the fifth-place Chicago Blackhawks.
The Senators (13-25-4) are last in the seven-team Scotia North Division, 13 points behind the fourth-place Montreal Canadiens.
The top four teams in each division will qualify for the playoffs.
