Jones, 29, suffered a thigh muscle tear in Pompey's 1-0 win at AFC Wimbledon on Tuesday and was replaced by substitute Brian Murphy in the first half.
Murphy is expected to start against Hartlepool on Saturday.
"Paul will unfortunately join our injury list, which seems to be growing and growing," Portsmouth manager Paul Cook told BBC Radio Solent.
Portsmouth have secured a place in the League Two play-offs and still have a mathematical chance of automatic promotion if they can win their remaining two games.
Portsmouth goalkeeper Paul Jones has been ruled out of the remainder of the club's League Two campaign.