Moult was named on the bench against home-town club Stoke, having been out of action since December 22.
But in the warm-up he felt his hamstring tighten and had to be replaced on the bench by Paul Huntington.
PNE manager Alex Neil said: “We had him scanned on Monday and unfortunately it has not come back with great news – he will be a few weeks.
“He’d had a full week’s training and felt fine so we put him on the bench at Stoke.
“But then it tightened up in the warm-up.
“The scan shows there is a little gap that we need to fix in the tendon.
“It’s not as bad as the injury was initially.”
Moult was among several players to be hit by hamstring injuries in December. Having scored the winner against Nottingham Forest, he was injured in training a few days later.
That forced him to miss the 3-2 win over Millwall but Moult returned for the clash with Sheffield Wednesday on December 22.
He lasted 47 minutes of the Hillsborough visit before pulling up injured.
North End have at least got more cover for Moult now than they had last month. Jayden Stockley arrived from Exeter and Sean Maguire is now back to fitness after his own hamstring injury.
On the fitness front, Tom Clarke is back training after missing the last two games with a calf strain.
That could bring him back into contention for Friday night’s Deepdale meeting with Derby County.
Neil said: “Tom is starting to come back – he’s trained this week, which is good.
“We are not looking too bad at the moment with the squad.
“Callum Robinson is the next one scheduled to come back in the first couple of weeks of March.”