Dunne suffered the injury during the 1-0 defeat by leaders Manchester City at Villa Park on Sunday after falling when challenging England goalkeeper Joe Hart for a cross.
"Richard Dunne sustained a fracture to his right clavicle (shoulder) in the game against Manchester City," a Villa statement said.
"He will undergo an operation today (Monday) in Birmingham. It is anticipated that he will be sidelined for up to eight weeks."
Sunday's defeat left Villa 15th in the table, seven points above the relegation zone.