The Australian Greens are concerned the federal government's royal commission into child sexual abuse lacks a focus on such activities in aboriginal communities.

Prime Minister Julia Gillard on Friday announced NSW Supreme Court judge Peter McClellan had been appointed to head the six-member royal commission into child sexual abuse in institutions.

"Our only concern is the absence of specific reference to Aboriginal abuse," Greens leader Christine Milne said in a statement.

"We certainly encourage the commissioners to ensure that they visit indigenous communities, examine the issues specific to them, and take into account the cultural sensitivities surrounding giving evidence."

Senator Milne said the Greens welcomed the establishment of the commission.