Johnson slumped to the turf in the first quarter of the match against the Gold Coast in Blacktown. The club believes he has ruptured his anterior cruciate ligament.
Results of scans are expected on Monday and the best course of action will then be determined for the 21-year-old.
"I was actually coming off the bench, but a few of the boys said they heard a snap," Swans co-captain Jarrad McVeigh said at the club's fan day at the SCG on Sunday.
"It's obviously shattering for him and you don't want to see that happen to anyone.
"It's disappointing for AJ and for the team. He's been a really consistent player for us over a short career and hopefully he can come back bigger and better.
"We might see him at the end of the year, I'm not too sure, but obviously it's not a great result."
The Swans do have some depth in the backline, with Tony Armstrong, Dane Rampe and Harry Cunningham impressing during the pre-season.
Lewis Roberts-Thomson can also comfortably slot into defence, while Nick Smith (knee) and Marty Mattner (hip) should return from injury over the coming fortnight.
But none of them possess the unique skill set that Johnson brings to the team.
"He's that good height, he's fit, he's fast, so you can't replace him," McVeigh admitted.
"But we've got guys that will certainly step up and will get their opportunity this week and the weeks to come to cement a spot in the team.
"We need those guys to do it.
"(Smith and Mattner) will have to come in now. With AJ going down they'll have to play this week and we'll put out our best side this week and get ready for round one.
"They'll probably play reserves as well, but they have to be ready."
The Swans face Port Adelaide at AAMI Stadium on Saturday in their final pre-season match before taking on Greater Western Sydney in round one.
Over 3500 fans turned up to the fan day on Sunday, more than double last year's crowd, and the club has set a goal of 40,000 members.
"I think we're up to about 30,000 members and we might break the record this year, which would be an unbelievable thing for this footy club," McVeigh said.
"We really need the support. It's a tough market in Sydney but we've got a lot of loyal fans in Sydney and in Melbourne.
"Great turnout today and hopefully we can see those guys in round one and round two playing in Sydney."
