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The plane had taken off from Imam Khomeini International Airport in the Iranian capital of Tehran, and was bound for Kiev.
However, flight data shows the Ukrainian Boeing 737-800 dropped to the ground just after it left.
Qassem Biniaz, a spokesman for Iran's Road and Transportation Ministry, said an issue arose when a fire struck one of the aircraft's engines. The pilot is then believed to have lost control of the plane, which was sent crashing into the ground.
Biniaz said that the plane was carrying 167 passengers and nine crew members.
A spokesperson for Iran's Aviation Corporation said: "When we received the news about the Ukrainian plane's crash, the emergency teams went to the crash location to find out the incident details and rescue survivors."
However, Pirhossein Koulivand, the head of Iran's Emergency Medical Services, explained that emergency crews had been dispatched to the crash site, but were unable to assist as the area was ablaze.
Ukrainian president Volodymyr Zelensky has also expressed his condolences to the victims and their families, and has said the embassy is working hard to find out more about what happened.
He said: "Terrible news from the Middle East. This morning, after taking off from the Imam Khomeini International Airport (Tehran), the passenger plane of Ukraine International Airlines crashed near the airport. According to preliminary data, all passengers and crew died.
"Our embassy is verifying data about the circumstances of the tragedy and the lists of the victims.
"My sincere condolences to families and friends of all passengers and crew."
Boeing said in a statement: "We are aware of the media reports out of Iran and we are gathering more information."
Tensions are high in Iran at the moment after the military fired more than a dozen rockets at two military bases in Iraq, which house US troops. The attack was in response to a US drone strike that killed Iran's top military commander Qassem Soleimani.
Speaking after the rocket attack, Iran's Islamic Revolutionary Guard Corps said in a statement: "The fierce revenge by the Revolutionary Guards has begun."
Iraq's Joint Military Command confirmed that several rockets had hit the American base at al-Asad, in Anbar Province, in western Iraq and the Erbil base in Iraqi Kurdistan.
The White House has released a statement: "The President has been briefed and is monitoring the situation closely and consulting with his national security team."
Local media reports the rockets hit the base at 1.20am, which was the same time Maj. Gen. Qassem Soleimani was killed last week.
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