Swans head of football Charlie Gardiner said Franklin had pulled up sore from training last week and hadn't recovered enough to train fully ahead of the trip to Hobart to take on the Kangaroos.
"Lance Franklin pulled up sore from our final training session last week and didn't get up for our game against Essendon," Gardiner told the club's website.
"Our medical team have said that he is probably more unlikely than like to play at this stage.
"I am not expecting Lance to take the field against North Melbourne."
Including the North game, Franklin will have missed four weeks with the hamstring complaint that first forced him out ahead of the Sydney derby against GWS in round six.
In better news, Sam Reid is expected to be fit to face the Kangas after recovering from a knock to his hip.
However, former Cat Daniel Menzel will need more time in the NEAFL to build fitness after his three-goal debut in Swans colours last weekend.