Morrison said Australia remained committed to finding a two-state solution to Israel's conflict with the Palestinians.
Israeli Prime Minister Benjamin Netanyahu said he had recently spoken to Morrison and welcomed the Australian policy shift.
US President Donald Trump recognized Jerusalem al-Quds as the "capital" of Israel last December and moved the American embassy to the ancient city in May.
Some of Judaism's holiest sites are located in the West Bank and eastern Jerusalem, including the Temple Mount and Western Wall in Jerusalem; the Tomb of the Patriarchs and Matriarchs in Hebron; and Joseph's Tomb in Nablus.
"Morrison's embassy announcement seems reckless and has the potential to be received poorly in nations such Indonesia and Malaysia", said Greg Barton, chair in global Islamic politics at Melbourne's Deakin University.
Opposition foreign affairs spokeswoman Penny Wong said the prime minister was playing "dangerous and deceitful" word games.
On the subject of a government review of the Iran nuclear deal, Morrison said: "These are obviously existential questions for countries like Israel and so I want to be satisfied - it's been three years now and I think it's timely to look at those issues and review our position and do that in a fairly systematic way".
Ambassadors from 13 Arab countries met in Canberra on Tuesday and agreed to send a letter to Australia's foreign minister expressing their concern, Egyptian ambassador to Australia Mohamed Khairat said.
Sharma, who was ambassador to Israel between 2013 and 2017, is on Saturday standing as a candidate for Morrison's ruling Liberal Party in a crucial by-election in Sydney.
Media reports have suggested that the possible shift in Canberra's foreign policy is related to the October 20 by-election in Wentworth, which has a Jewish community of about 12.5 percent.
The U.S. Embassy became the only foreign embassy in Jerusalem in May, but Netanyahu has attempted to persuade others to follow suit.
Morrison denied that the United States or the by-election had influenced his announcement.
He said no decision had been made and he was simply being open to the suggestion.
While the Palestinians insist on drawing the demarcation lines along the 1967 borders, with East Jerusalem serving as the capital of the future Palestinian state, Israel claims historic rights to the entire city.
Jerusalem is also a holy city for the largely Muslim population of the Palestinian territories, and they feared that recognition of the city as a Jewish capital would imperil shared access to the many religious sites. Peace talks between the parties broke down in 2014.