Mr Henning, a former taxi driver from Manchester, was kidnapped last December in Syria by Islamic State (IS) militants.
The aid worker, aged 47, was shown at the end of a video last week after the beheading of fellow British captive David Haines.
Mr Henning’s wife Barbara said she has sent messages to IS asking them to release her husband but has had no response.
In a statement released through the British Foreign Office she said: “Alan is a peaceful, selfless man who left his family and his job as a taxi driver in the UK to drive in a convoy all the way to Syria with his Muslim colleagues and friends to help those most in need.
“When he was taken he was driving an ambulance full of food and water to be handed out to anyone in need. His purpose for being there was no more and no less. This was an act of sheer compassion.
“I cannot see how it could assist any state’s cause to allow the world to see a man like Alan dying.”
It is the first time Mr Henning’s family has issued a public statement since he was threatened in the IS video earlier this month.
The group previously released footage of the killing of US journalists James Foley and Steven Sotloff.
A separate video released this week showed British photojournalist John Cantlie reading a prepared script and explaining he would speak about IS in future videos. No threat to kill Mr Cantlie was made on camera.
Pleas for the release of Mr Henning have been made by high-profile Muslim leaders in recent days, warning IS that the killings and threats are against Sharia law.
Renowned Jihadi ideologue Muhammed al-Maqdisi and the family of jailed Pakistani scientist Dr Aafia Siddiqui, whose release has been demanded by IS extremists, have also called for Mr Henning to be freed.