Farriss, 57, caught his left hand while operating a winch on his boat in Sydney last month, severing his ring finger.
He has undergone surgery twice to try to reattach the finger but has been left with permanent hand damage.
In an email to his brothers and bandmates he reportedly said the situation was "horrific".
"I don't know if I will be able to play properly again," local media quoted him as saying.
The band's manager, Chris Murphy, said Farriss was now home and undergoing physiotherapy to help him regain some movement
"He is getting the best possible care and we hope with time he will regain movement in his finger. This was a terrible accident, we are all here to support him."
Farriss has since thanked fans for their messages, posting on Facebook that he was "overwhelmed by the outpouring of love and well wishes".
"Thank you all, I'm feeling the love and it's really helping me get through this nightmare."
Farriss is a founding member of INXS, which was one of the world's biggest bands in the 1980s and 1990s.
The Australian band stayed together after the suicide of frontman Michael Hutchence in 1997, taking on a series of guest singers.
They officially retired in 2012 but their "Very Best" album, released in 2014, became Australia's top-selling album that year.
INXS guitarist Tim Farriss has said he may never play the guitar properly again after severing his finger in a boating accident.