Sunderlands promising young goalkeeper
The 22-year-old Englishman sustained the injury during his side's 3-1 defeat at Manchester United on Boxing Day.
Initial fears he had ruptured his anterior cruciate ligament, which could have ended his season, have proved unfounded.
"Jordan has good news and bad news," Moyes told a press conference ahead of his side's trip to Burnley on Saturday. "The good news is he hasn't ruptured his ACL. The bad news is he's strained it.
"We're looking at six to eight weeks. It's a major disappointment for him and for us because he's been saving us points."
Sunderland are currently third from bottom in the Premier League table, two points from safety.
An eight-week lay-off would see Pickford miss at least seven league games, as well as Sunderland's FA Cup third-round tie at home to Burnley a week on Saturday.
Italian Vito Mannone, who started the season as Sunderland's first-choice goalkeeper before succumbing to an elbow injury, is expected to deputise.