The 26-year-old had re-signed for the Red Rose club for the 2017 T20 Blast, which he helped them win in 2015.
But Lancashire have not received the necessary paperwork from Cricket Australia to allow him to rejoin.
"The decision has been taken for me to rest up in July and August," said Faulkner.
"This will undoubtedly be in my best interests but I am sorry to be missing out on more playing time with Lancashire."
Faulkner, who has played one Test, 67 one-day internationals and 24 T20 matches for his country, has a central contract with Australia.
Cricket Australia believe his knee injury requires ongoing management and have refused to issue the No Objection Certificate (NOC) required for him to play in the English county game.
Lancashire head coach Glen Chapple added: "It's disappointing that James won't be re-joining us, but we understand the reasoning from Cricket Australia.
"We'd had some indications of Faulkner's position and so we worked hard on bringing Junaid Khan as his replacement. We are also confident of securing another addition to the squad in the coming weeks."
Australia all-rounder James Faulkner has been refused permission to play for Lancashire this summer by his country because of an ongoing knee injury.