The drummer’s mother announced the news of Green’s diagnosis in a Facebook post on Christmas day.
“Please send healing vibes for my son…who is battling stage four cancer” wrote Carol Namatame on Sunday 25 December.
Green’s friend, and Seattle radio DJ Marco Collins also also shared the news on a Facebook post of his own.
Green, who has been an ongoing member of the band bar a short hiatus between 2003 and 2004, began the group’s recent tour but was forced to leave early due to his illness.
Modest Mouse were founded by Green, frontman Isaac Brock and bassist Eric Judy during the nineties.
The band are most famous for hits such as 2004’s “Float On” and 2007’s “Dashboard”.
Earlier in the year, frontman Brock teased new music , telling NME at the time that he “got seven new songs coming out pretty soon”.