He is set to meet and hold consultations with his counterparts from several countries on the sidelines of the event, IRNA reported.
The US issued visas on Thursday for Zarif and President Hassan Rouhani, who is slated to set off for the UN headquarters on Monday.
Several members of the US Congress had called for denying visas to both men after last Saturday's attack on the Saudi oil infrastructure, which senior officials from US President Donald Trump's administration have blamed on Iran, according to Financial Tribune.
Iran and the US have been engaged in a standoff over the 2015 nuclear deal since last year, after Trump pulled out of the accord and reimposed sanctions on Tehran.
Tensions between the two foes had already begun to escalate after tanker attacks in the Persian Gulf in May and June that Washington also blamed on Iran and called for the launch of an international security mission to protect free shipping in the strategic waters.
On Thursday, US Secretary of State Mike Pompeo said the United States was seeking to build a "coalition aimed at achieving peace and a peaceful resolution".
"Coalition for Peaceful Resolution?" Zarif tweeted, listing eight diplomatic initiatives by Iran since 2015, including a peace plan for Yemen and a regional non-aggression pact for the Persian Gulf region proposed earlier this year.
The 74th session of the UN General Assembly opened on Tuesday and the high-level General Debate is due to start on Sept. 24, where world leaders and diplomats from 193 nations will come together to address a range of pressing issues.
Climate change is the top ticket item on the UNGC’s agenda this year.
During the week, a host of other high-level events will also convene, including on climate change, Universal Health Coverage and sustainable development.