Scans revealed a fracture, and an apologetic Marsh said he faced up to six weeks on the sidelines.
That would almost certainly rule him out of the opening Test against Pakistan in Brisbane starting on November 21.
"It's my middle finger, just below the wrist - a fracture straight through the bone," Marsh, who was sporting a cast on his arm, told reporters.
Asked if he had spoken to Langer, Marsh replied: "He just told me I'm an idiot basically."
Marsh had only been recalled to the Test side for the final game of the Ashes against England last month after a long period out of favour and there are no guarantees he will win a spot back.
"It's a good lesson for me. Hopefully it's a good lesson for other people as well," added Marsh, whose blunder could open the door for Marcus Stoinis in Brisbane.
"At the end of the day, it's a game of cricket. Sometimes you get beaten, sometimes you get out, and you can't be punching walls."