Their hopes of a 16th consecutive finals berth now hinge on five consecutive wins to finish the regular season and even that may not be enough.
Grant is set to miss at least some of the fight for Melbourne's season, joining big names Cameron Munster, Xavier Coates, Eli Katoa, Tui Kamikamica and Will Warbrick on the pine.
The Queensland hooker pulled up sore popping a pass up for Trent Loiero just before halftime in Friday's clash at Accor Stadium.
He limped to the sidelines and threw his headgear to the ground in frustration.
After a torrid week that claimed David Fifita (suspension), Cam Murray (calf) and Tallis Duncan (hamstring), the Rabbitohs lost their own hooker Brandon Smith (calf) to injury.
But the victory was crucial to South Sydney's own finals hopes, which had been thrown into jeopardy with two losses from their previous four games.
Souths were staring down the possibility of falling out of the top eight to finish the weekend when Tyran Wishart and Nick Meaney crossed in quick succession during the final 15 minutes.
Right centre Meaney scythed over to give the Storm a two-point lead with 10 minutes to play.
But when fullback Sua Fa'alogo, excellent to that point, fumbled Cody Walker's 40/20 kick into touch, the home side had the chance to strike back.
Recently re-signed halfback Ashton Ward found Campbell Graham with a beautiful cutout pass on the right side to give Souths a two-point lead that they held.
Fa'alogo had been essential as Melbourne, down 8-0 after as many minutes, rallied for a 16-8 halftime lead.
Most memorably, he beat four defenders then turned rival fullback Matt Dufty inside out on an 80-metre tear for the visitor's third try.
But without Grant patrolling the middle of the park, the Rabbitohs snatched back ascendancy in the second half and began to pick apart the Storm's edges - a defensive weakness for the Melburnians all year.
Ashley Klein became the most-capped NRL referee, officiating his 444th game.
6°C