The full-back limped off late in Sunday's 2-1 defeat at home to Manchester United after falling awkwardly and appearing to twist his right leg.
Liverpool have yet to confirm the extent of the problem but Kelly himself does not expect to be back for at least three months.
"What I can say is its not the worst injury I've had, and for sure I'll be fighting for my place next year when I'm back fitter and stronger!" he wrote on Twitter.
Manager Brendan Rodgers' injury concerns do not end there with centre-back Daniel Agger awaiting the results of a scan on suspected medial ligament damage in his left knee, while forward Fabio Borini has a bruised foot and swollen ankle after the United game.