Hamas denies that the film is officially sanctioned by them.
Hamas spokesman Mahmoud Zahar said that the film, which was released by the group’s military wing, “does not reflect the official position of Hamas”.
Mr Zahar said: “We have not killed in the past and will never kill captive Israeli soldiers. Our morals prevent us from doing so."
The animated film shows Gilad’s father, Noam Shalit, campaigning for his son, who has been held in the Gaza Strip for three years.
The voice of the soldier on the film is taken from the latest real video of Gilad Shalit, which Hamas released last year to prove he is still alive.
The animation shows an ageing Noam Shalit, walking past posters of different Israeli prime ministers, each promising to secure Gilad’s release, to show the passage of time.
Mr Shalit is then seen waiting at the Erez border crossing, and screams “No!” as a coffin draped in an Israeli flag emerges from a military car.
The video then displays the Izzadim A-Qassam Brigades symbol, with the text “There is still hope”.
Mr Shalit has condemned the video, saying: “It is a shame that Hamas leaders continue to choose psychological warfare for the who-knows-what time against our family, and against the Israeli public, instead of addressing and authorising the prisoner swap deal that has been on their table for four months with no response.
"The Hamas leaders would do well if they stopped producing films and installations, and took care of the real interests of the Palestinian prisoners and the simple Gaza residents, who have been held hostage by their own leaders for a long time.”
Mr Netanyahu said: "It is yet another despicable action aimed to help the Hamas leadership avoid making a decision regarding our offer for a prisoner swap deal which it has not responded to for many months.”