"Jordan has good news and bad news," Moyes told a news conference on Thursday. "The good news is he hasn't ruptured his ACL (anterior cruciate ligament); the bad news is he's strained it.
"We're looking at six to eight weeks. It's a major disappointment to us and more importantly for the boy. He's been saving us points recently."
Moyes said the 22-year-old, who is likely to be replaced by Vito Mannone in goal, did not understand the severity of the injury during the game.
"He didn't realise. After the game I saw physios working on him and you tend to think it must be okay," the manager added.
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"Jordan has been one of the brightest young prospects in England right now. I know there's been a batch of very good players coming through but I saw Jordan as one of the best ones."
Defender Javier Manquillo and midfielders Jack Rodwell and Steven Pienaar are back in training for the trip to Burnley, but Moyes' options will be cut further in January when Lamine Kone, Wahbi Khazri and Didier Ndong head for the African Nations Cup.
The team are already battling an injury crisis, with Paddy McNair and Duncan Watmore out for the season, and Lee Cattermole, Jan Kirchhoff and Lynden Gooch not expected to return until the middle of March.
Despite their troubles, Sunderland have won three of their last five games and Moyes urged his players to dig deep and get a win at Burnley.
"Turf Moor has always been a difficult place to go," he added. "Burnley have some really good results on the board but we're getting closer.
"They've picked up some big wins at home so we'll be mindful of that, but we'll go there and try to win. We've slowly climbed our way up the table but we need to keep climbing. We've been here before, that experience will help us."
(Reporting by Simon Jennings in Bengaluru)
