Uncapped Edinburgh quartet Ross Rennie, Calum MacRae, Ben Cairns and Nick De Luca are called up, along with Glasgow winger Thom Evans and prop Moray Low.
Centre Marcus di Rollo, prop Craig Smith and hooker Scott Lawson are also left out.
Hadden said: "It is definitely not all over for Scott, the door is never closed.
"It is important to understand that it is a training squad for Monday, not for the 6 Nations.
"There will be an opportunity for a number of guys who are not included who have been part of the squad before. The key to the second row is competition.
"Scott has done well in France but we've got young guys champing at the bit who are playing well too, so the opportunity is there for them to show what they can do.
"There will be changes to the squad before the 6 Nations begins.
"Scott has made a massive contribution in the past and can do so again.
"I spoke to him before I released the squad and he was determined, committed and reflective and wants to fight his way back in to the team in the days and weeks to come."
Hadden confirmed Jason White would continue as Scotland captain.
"Jason is a key figure for us," he said. "He sets the tone as a leader both on and off the field and I look forward to working with him again during this season's championship."
Centres Rob Dewey and Andrew Henderson will attend the squad gathering on January 14 despite carrying injuries, as will Stade Francais number eight Simon Taylor, who has a thumb problem.
However, Northampton winger Sean Lamont is out for the rest of the season with knee ligament damage.
Di Rollo has made the decision to make himself available exclusively for Toulouse during the tournament but has stressed that he will battle for a place after the 6 Nations.
The centre has managed just one minute of game time since his post-World Cup move to France from Edinburgh.
"Making myself unavailable for Scotland for this year's 6 Nations Championship was not a decision I took lightly," he said.
"After a period of injury and transition from Scotland to France I felt it would be beneficial for my game to take some time to settle in to my new club."
Centre Cairns, 22, is listed in the senior Scotland squad for the first time, while Ulster winger Simon Danielli returns after missing the World Cup through injury.
"I continue to be impressed with the competition for places in the squad," added Hadden.
"A number of players have maintained their good form from the World Cup but they are going to be pushed extremely hard by some of our young, up and coming talent in the next few weeks."