"Obviously the timing for this isn't ideal, but Billie Joe's well-being is our main concern," band member Mike Dirnt said in a posting on Green Day's website.
"We are happy to say that Billie Joe is doing well, and we want to thank you all for the outpouring of support and well wishes that we have received, and we can't wait to see you all again soon," he added.
Armstrong, lead singer and guitarist for the Grammy-winning rock band, sought substance abuse treatment late last month following an angry, guitar-smashing on-stage outburst in Las Vegas. Details of his substance abuse have not been released.
Green Day also announced on Monday it was moving up the release date of "iTré!," part of an ambitious trilogy of albums that marks their first collection of new music since 2009, to December 11 from its original date of January 15, in part to make up for the canceled and postponed dates.
"If we couldn't be there to play it for you live, the least we could do was give you the next best thing," said drummer Tre Cool.
The band's latest tour, including dates in Seattle, Sacramento and Reno, was due to wind down in Tempe, Arizona, on December 10. The website said tickets for the club shows would be refunded, and that new dates for the postponed shows would be announced shortly.
The California-based punk rock band, formed in the late 1980s, has sold more than 65 million records worldwide and won five Grammys, including best alternative album for its 1994 major-label debut, "Dookie," and best rock album for "American Idiot" and "21st Century Breakdown."
(Reporting by Chris Michaud; Editing by Jill Serjeant, Gary Hill)
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