Warren Gatland's squad will begin the recovery process on Monday from a sobering 29-18 Twickenham defeat against title contenders England.
But they will host the Scots without full-back Halfpenny, who scored all of Wales' points in a goalkicking masterclass and then dislocated his shoulder helping to thwart an England try.
"Leigh has dislocated his shoulder, so I think that's him gone for the rest of the season," Gatland said.
"That will be Leigh's season over, which is disappointing for him."
Scrum-half Rhys Webb also left the action early, limping off with a suspected ankle injury, suggesting a minimum of two changes when Gatland names his team to face Scotland on Tuesday.
There are likely to be other switches, though, such was the paucity of Wales' performance, with fly-half Rhys Priestland and prop Gethin Jenkins among those likely to be sweating on their places.
"It has been tough on these players in retrospect - a Grand Slam (2012), a championship (2013) and a Lions tour. It has been a long 18 months for those players," Gatland added.
"But this is professional sport and you've got to get yourselves up, and unfortunately we weren't as good as we can be. That is disappointing.
"Teams are pretty close in this competition. I think the four top teams are all capable of beating each other on their day if they get their performance right, and England got their performance right."
Wales beat England by a record 30-3 margin in Cardiff last season, yet they never threatened to triumph this time around as hopes of an unprecedented Six Nations title hat-trick were destroyed.
Skipper Sam Warburton said: "That game, the 30-3 last year, was just one of those games where everything clicks for you. That happens once in a blue moon.
"That happened for us last year, but this year England deserved the win."
Wales were rocked by an early Danny Care try, and they never really recovered as England ended a run of three successive defeats against their fiercest rivals.
"It was a disappointing result," Wales number eight Taulupe Faletau said.
"There were too many errors, and England capitalised and scored points. They built momentum up pretty quickly, and we couldn't quite get there.
"We are out of contention for the championship now, but we want to end with a win and on a good note next Saturday.
"Going into the championship we wanted to come away with the title, and we haven't been able to do that. It is disappointing."
- Sports & Recreation
- Warren Gatland
- Rhys Priestland