Heskey suffered the setback in training Wednesday and will require surgery.
The former England player has started the season in fine form and is joint leading scorer with four goals.
It is another striker setback for Villa boss Gerard Houllier, as Gabriel Agbonlahor is still recovering from groin surgery.
John Carew, who has struggled to make an impact so far this season, is the club's only fit senior frontman ahead of Saturday's Barclays Premier League clash at Fulham.
England Under-19 player Nathan Delfouneso will also be in contention to face the Cottagers.
Heskey, who quit international football after the World Cup this summer, has been revitalised since the arrival of Houllier as Martin O'Neill's successor.
The former Liverpool player has finally started to win over the Villa fans after adding goals to his performances.
A club statement read: "Emile Heskey will miss the clash with Fulham after picking up a knee injury.
"Heskey tore the medial meniscus in his right knee Wednesday in training with no other player involved in the incident. The injury will require an operation and he faces between three to four weeks out of action."