Galloway also missed the end of last season, having ruptured the Achilles tendon in his other leg.
The 31-year-old's latest injury will also rule him out of Scotland's squad for the World Cup starting in October.
Galloway has made 43 appearances for Leeds since joining from NRL side Wests Tigers ahead of last season.
Leeds Rhinos prop Keith Galloway will miss the rest of the season after rupturing his Achilles tendon in the Super League win over Hull FC.