Crichton landed awkwardly in a tackle involving Rabbitohs duo Campbell Graham and Jack Wighton in the 43rd minute and failed to return to the field on Friday.
Dogs coach Cameron Ciraldo said Crichton had suffered a grade two AC joint injury, which would rule the Samoa international out of facing former club Penrith next Thursday.
Canterbury (2-2) meet the Panthers, Parramatta, premiers Brisbane and North Queensland over the next month.
"It's not looking great in there," Ciraldo said.
"They (the medical team) are saying a high grade two, grade three possibly AC - that's the initial thoughts on it so he'll be out for a while.
"It's an opportunity for someone else."
At the time their star centre went down the tunnel at Accor Stadium Canterbury were leading 18-12.
But they finished the second half by completing just 40 per cent of their sets, conceding six penalties and making 12 errors.
Only a late try to fullback Connor Tracey prevented Souths from keeping the Bulldogs scoreless in the second half.
Ciraldo resisted the chance to throw disgruntled centre Bronson Xerri in as a straight-swap replacement for Crichton, instead shifting five-eighth Matt Burton to centre and bringing Sean O'Sullivan into the halves.
"Bronson was there covering the wing and centre but when you lose your best communicator," Ciraldo said.
"I needed to get another communicator out there, and Sean's one of the best at that."
But after the reshuffle, the Dogs lost all fluency in attack as Souths laid on 20 second-half points to claim a third win from their opening four games.
Latrell Mitchell grabbed two tries and kicked six goals, finishing the match at fullback after Jye Gray went off for a head injury assessment.
Souths coach Wayne Bennett said Gray passed his test and will be fit to face Canberra next week, but admitted to concern over Keaon Koloamatangi who picked up a suspected medial ligament injury.
Souths raced into an early lead in front of a crowd of 49,813 when Alex Johnston picked off a Tracey pass and ran 90m to score in the fifth minute.
Marcelo Montoya and Mitchell traded tries before Canterbury hit the front foot just before the break.
Lachlan Galvin dived on his own kick to the in-goal as a rampaging Sitili Tupouniua crashed over to make it 18-12 at the break.
But after Crichton's injury, Canterbury fell apart with Cameron Murray, Tallis Duncan and Mitchell pulling Souths out of sight.
"We played somewhere near our potential and what we've got in the team," Bennett said.
"The last time we played we were far off that - we weren't perfect today, but we look closer to where we want to go."
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