The execution of two Australian drug traffickers, spying revelations and the poor treatment by Indonesia of live cattle imports lay behind the tensions.
Trade and economic relations are expected to dominate discussions with Indonesia’s President Joko Widodo.
Mr Turnbull’s visit is part of a five-nation tour.
He will also visit Germany, Turkey, the Philippines and Malaysia.
Ministerial ties between Australia and Indonesian cabinet members only resumed in August this year, shortly before Mr Turnbull came into office.
They had been suspended following the execution in Indonesia in April of Andrew Chan and Myuran Sukumaran, two Australians convicted of drug smuggling.
Australia’s policy of turning around boats of asylum seekers, many of which had departed from Indonesia, also caused tension.
Despite this Australia’s Department of Foreign Affairs and Trade describes the relationship with Indonesia as “one of Australia’s most important”.