Mr Goldberg-Polin, born in California, was kidnapped from the Supernova festival, where he lost an arm in a grenade attack.
The video was likely made under duress, and Mr Goldberg-Polin appeared sickly, pale and thin as he read at least part of his statement from a teleprompter.
It was not clear when the video was recorded but it appears to have been very recent as Mr Goldberg-Polin spoke about 200 days of captivity, which he would have marked earlier this week, and the festival of Passover, which began on Monday evening. He spoke about living in “underground hell without water, food, sun or medical treatment”.
He said at least 70 of the remaining 130 or so hostages had been killed in Gaza in Israeli bombings, likely repeating a line given to him by his captors. Official Israeli estimates have put the number closer to 35.
A White House spokesman confirmed it had received the video, the first Hamas has publicly released of a US hostage.
An official said the FBI and hostage rescue experts have been analysing the footage to ascertain if they can glean anything from it.
Mr Goldberg-Polin, whose family has been one of the most active advocates of a hostage deal with Hamas, said Benjamin Netanyahu and his government “should be ashamed of themselves” for not stopping the war in Gaza.
Mr Goldberg-Polin told his parents in the video “I love you and I miss you so much” and wished them a happy Passover.
His family have mounted a campaign pushing for his release, with posters showing him smiling and displaying the slogan “Bring Hersch home” often seen on the walls of Israeli towns.
His family did not have an immediate comment but said it would release a statement later.