Hoggard, who is likely to be sidelined for a month-and-a-half, bowled just three balls for Yorkshire in a cup game on Wednesday against Worcestershire before being forced to leave the field. A scan revealed a torn cartilage in his right knee.
England and Wales Cricket Board chief medical officer Peter Gregory said: "Matthew will need to see a surgeon to find out if an operation is required. Our initial assessment is that he is likely to be out of cricket for approximately six weeks."
Hoggard's absence may force England to go into the second Test with an even more inexperienced bowling attack than they fielded in the first.
The 20-year-old James Anderson, in his first Test, led that attack and was backed up with Hoggard (19 Tests) and Steve Harmison (six Tests).
Strike bowler Andy Caddick (foot) and all rounder Andrew Flintoff (shoulder) are both injured and will not feature in the series, while Darren Gough is still working his way back from serious long-term knee problems.
After a fine start to his international career, Hoggard has been struggling for form in recent months and did not play in the World Cup.
The 26-year-old was included in the team for the first Test against Zimbabwe at Lord's, taking three wickets in the first innings as England won by an innings and 92 runs, but was not considered for the one-day side earlier this week.