The band did not disclose details about Armstrong's illness but had been scheduled to perform at the I-Festival on Sunday.
Armstrong's bandmates, Mike Dirnt and Tré Cool, later released a video statement to offer their apologies to fans.
"We apologize profusely," Dirnt said.
"Billy got rushed to the hospital last night due to illness. The doctors don't think it's a good idea for him to play today."
"We're beyond devastated," Tré Cool added. "We're as sad as you guys are. Billie's extremely upset about it, and we'll see you very soon."
The band is set to release a trio of albums—appropriately titled ¡Uno!, ¡Dos! and ¡Tré!—starting Sept. 25.