Under changes to the Australian Citizenship Ceremonies Code to be introduced in the first half of 2019, councils must hold a second citizenship ceremony on September 17 - Australian Citizenship Day.
Local councils said they are listening to community concerns about Indigenous cultural sensitivities, with the date marking the arrival of British explorers.
Mr Morrison said his announcement is "commonsense", warning that local councils risked violating the new standards at their own peril.
"Australia Day is for all Australians and councils are given the right to hold citizenship ceremonies by the Commonwealth government. And Australia Day, of all days, in a country that is the most successful migrant country on earth should be the day that you should have the opportunity to be provided with your citizenship," he said.
Mr Morrison said he did not agree with Opposition Leader Bill Shorten's assessment that he was "playing politics".
"Now if councils don't want to do that -- as we have seen some of them do want to play games. Well, you don't have to run citizenship ceremonies. Other arrangements can be made.
"But we're not just going to cop people undermining Australia's national day...This is a pretty commonsense idea. I think it has broad support."
Labor leader Bill Shorten said 530 of Australia's 537 councils already held citizenship ceremonies on Australia Day.
"You sort of know when Australia Day's coming up don't you when a couple of weeks before we get the annual conservative outing to put politics into Australia Day," Mr Shorten told reporters in Melbourne on Sunday.
"It's what the conservatives do to keep their base happy."
NSW Premier Gladys Berejiklian said January 26 was the natural day for ceremonies to be staged.
"I think most people are excited to become Australian citizens and what better day to do that than on Australia Day," she told reporters in Sydney.
Some people staunchly oppose the current date, with thousands attending Invasion Day rallies to highlight it as offensive to Aboriginals and Torres Strait
But there is little political appetite for shifting Australia Day, with both major political parties committed to the status quo.