The Wilco frontman had been taking the medication to treat his migraine headaches.
Due to Tweedy's treatment, the Chicago band's album "A Ghost Is Born" has been pushed back to a June 20 release date. It was originally scheduled to hit stores on June 8.
It is still unclear what effect this will have on the band's plans for an upcoming tour.
The band is currently booked for a May 1 performance at the Coachella Valley Music & Arts Festival and a June 11 performance at the Bonnaroo festival in Manchester, Tennessee.