The doco is a VICE Studios production, "in association with VICE World News and Endeavor Content", a spokesperson for the media company said.
The Ukrainian government said in a Facebook post that it was "grateful" Penn was there, lauding him as being "more courageous" then Western leaders.
"An American actor and filmmaker, Oscar winner Sean Penn arrived to Ukraine. The director specially came to Kyiv to record all the events that are currently happening in Ukraine and to tell the world the truth about Russia's invasion of our country.
"Sean Penn is among those who support Ukraine in Ukraine today. Our country is grateful to him for such a show of courage and honesty.
"This morning the director visited the Office of the President and visited the press briefing of the advisor of the head of the Office of the Head of State Mikhail Podolâk and the Vice Prime Minister - the Minister of the Reintegration of temporarily occupied territories of Ukraine Irina Vere щуuk.
"He spoke to journalists, to our military, saw how we defend our country.
"Sean Penn demonstrates the courage that many others, especially western politicians lack. The more such people, true friends of Ukraine, who support the fight for freedom, the sooner it will be possible to stop the massive attack by Russia."
Earlier this week, Penn was spotted out having dinner in Kyiv with other journalists.
While he settles in, thousands of others are desperately trying to flee the country.
Thousands of people sheltered in underground subway stations to escape the chaos, while Americans stranded there boarded buses to leave for Romania or Poland.
