More than 370,000 Rohingya have fled to Bangladesh to escape violence since August 25, according to the United Nations, an average of almost 20,000 a day.
A spokesman for the presidential office said Wednesday that Suu Kyi had called off her trip for two reasons.
"One is the current situation in Rakhine state. We have terrorist attacks and also there are many works on public safety and humanitarian works," spokesman Zaw Htay said in a statement.
"And the second reason is we have received reports that there are possibilities of terrorist attacks in our country."
Htay later announced Suu Kyi would give a "state of the union" speech next Tuesday in which she would address the Rohingya crisis fully.
"She will explain about everything ... Her speech is not only for the country but to tell the world as well," he told reporters.
One of the world's largest annual diplomatic occasions, the 72nd UN General Assembly opened Tuesday in New York, with events expected to last for weeks, including a speech by President Donald Trump. Suu Kyi isn't the president of Myanmar; her official title is state counselor
in the country formerly known as Burma.
The latest outbreak of violence in Rakhine state was sparked last month by a series of alleged attacks by Rohingya militants on government border posts.
The actions of Myanmar's armed forces are a "textbook example of ethnic cleansing," UN human rights chief Zeid Ra'ad Al Hussein said Monday. They are believed to have intensified following the recent attacks.
Suu Kyi criticized for response
Refugees are pouring across the border into Bangladesh, bringing with them stories of murder, rape and devastation.
Suu Kyi has been repeatedly criticized over her response to the crisis, particularly given her previous work as a defender of human rights
for which she won the Nobel Peace Prize
During her last speech to the United Nations in September 2016, Suu Kyi said her government didn't fear international scrutiny
over its handling of the Rohingya.
"We are committed to a sustainable solution that will lead to peace, stability and development for all communities within the state," she said then.
By October, new violence had broken out across Rakhine state.
Tom Malinowski, former US assistant secretary of state for democracy, human rights and labor, said he's "very sad" about Suu Kyi's response to the Rohingya crisis.
'They are suffering, these people'
On Tuesday, Bangladeshi Prime Minister Sheikh Hasina visited some of the hundreds of thousands of Rohingya refugees taking shelter in her country, condemning "those who are responsible."
"What is the crime of the women and children or the innocent people?" she asked. "Because these people, innocent people, children, women, they are suffering, these people, they belong to Myanmar. ... How can they deny they are not their citizens?"
But Hasina also blamed the insurgents who have struck out against Myanmar authorities, saying they should have worked with the government.
Hasina was one of 56 Islamic leaders to condemn the violence against the Rohingya in a joint statement Tuesday after an emergency meeting of the Organization of Islamic Cooperation
, the world's largest Muslim body.
The statement called for a "thorough and independent investigation" into the violence.
The leaders of Turkey, Pakistan and Iran were among the signatories.
It wasn't only Muslim countries defending the Rohingya, however. In a statement posted online, al Qaeda threatened the Myanmar government, calling for militants to "set out for Burma."
"The savage treatment meted out to our Muslim brothers ... shall not pass without punishment, and the government of Myanmar shall be made to taste what our Muslim brothers have tasted," the terrorist group said in a statement from its media wing, al Sahab.
UN meeting planned on Myanmar violence
The UN Security Council will meet Wednesday to discuss the ongoing crisis inside Rakhine state, which the organization says has left at least 1,000 dead.
The Myanmar government says the death toll stands at 421, including 378 "terrorists" and 28 civilians.
Sweden and the United Kingdom requested the meeting, saying in a statement they were "deeply concerned" by the reports emerging from Myanmar.
"It is important that the Security Council play its role in responding," Swedish Ambassador Olof Skoog said. "The priority is now to obtain immediate humanitarian access to those in need."
Skoog called for an end to the violence and protection for civilians from the fighting.
The United States expressed further concern about the ongoing Myanmar violence Tuesday, with White House press secretary Sarah Sanders saying the Trump administration was "deeply troubled."
In an earlier statement, the US State Department stopped short of condemning the Myanmar government or Suu Kyi for the crisis, saying instead it was "concerned."