Scans have confirmed the 19-year-old has damaged medial ligaments in his right knee and he will see a consultant on Monday.
The promising defender, operating in a midfield role in recent weeks, sustained the injury in last week's goalless home draw with Colchester and is expected to be out for up to six weeks.
"It's a blow for us and for Jack because of the form he had been in," Pools manager John Hughes told the club's official website.
"We're hoping that Jack is a quick healer and can be back quicker than expected, but we can't rush him so we'll make sure when he does return that he's 100 per cent right."
Baldwin, who made his first-team breakthrough last season, has started the last nine games, playing a key role in midfield as the club have stepped up their bid to escape relegation.
"It gives the opportunity for others to come in and show what they can do," added Hughes.
"But it is disappointing for Jack given that he had enjoyed a good run in the side."