Rousseff's trip comes just four days after the lower house of Congress sent impeachment proceedings to the Senate, which is expected to vote on opening a trial by mid-May.
Rousseff is going to the United Nations to sign the climate deal on Friday, but a government official told AFP that her speech would include "one sentence" about the political crisis back home.
The opposition has already warned the leftist leader against criticising the impeachment process, which she has described as a "coup," while she is abroad.
Rousseff decided to go to New York even though she had cancelled her attendance at the ceremony to light the Olympic flame in Greece on Thursday ahead of the Summer Games in Rio de Janeiro in August.
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Her trip means that Vice President Michel Temer, whom she accuses of conspiring to oust her, will be in charge of the country until her return, due late Friday or early Saturday.
Rousseff says charges that she used illegal accounting tricks to mask budget deficits have no legal basis.
After that, a two-thirds majority vote would be enough to oust her permanently, leaving Temer to serve out her term, which ends in late 2018.