The message doesn't give a reason for the cancellations:
Furthur had only one upcoming show on its schedule, an appearance at the Lockn' Music Festival in Virginia in September, while Ratdog had numerous dates scheduled for the coming months.
Ratdog took the stage without Weir last month for an appearance in Las Vegas, according to JamBase. A statement from the venue said Weir was "under the weather."
Weir, 66, also collapsed on stage in April 2013.
The announcement comes a day after the 19th anniversary of the death of Jerry Garcia, another founding member of the Dead. Garcia died of a heart attack on Aug. 9, 1995 after a long battle with addiction and numerous health problems.
CORRECTION: An earlier version of this article misspelled the name Furthur.