While onstage at a concert in Sydney on Sunday, Gass was presented with a birthday cake and asked to "make a wish" by Black.
Gass responded, "Don't miss Trump next time," an apparent reference to the rally shooting a day before that left the former president with an injured ear.
The video of Gass was widely circulated on social media.
"I was blindsided by what was said at the show on Sunday. I would never condone hate speech or encourage political violence in any form," Black said in a Tuesday statement on Instagram.
"After much reflection, I no longer feel it is appropriate to continue the Tenacious D tour, and all future creative plans are on hold. I am grateful to the fans for their support and understanding."
Following Black's statement, Gass apologised on Instagram.
"The line I improvised Sunday night in Sydney was highly inappropriate, dangerous and a terrible mistake," he wrote on Tuesday.
"I don't condone violence in any kind, in any form, against anyone. What happened was a tragedy, and I'm incredibly sorry for my severe lack of judgement."
The band recently completed dates in the US and Europe.
Their Spicy Meatball Tour was slated to continue on Tuesday night in Newcastle, hitting most major cities in Australia and New Zealand this month before returning to the US for a select few dates in October.
"Frontier Touring regret to advise that Tenacious D's concert tonight at Newcastle Entertainment Centre has been postponed," their touring company announced in a statement on Instagram Tuesday.
"Ticket holders are asked to hold onto their tickets until further information is available."
When asked for further comment, a representative for the band directed the Associated Press back to Black's statement.
Details on refunds for the remaining tour dates were not immediately available.
