After his discharge, Jensen worked for a short time as a barman in Truro, then as a marine store dealer in Adelaide.
He married Katy Herman (née Arthur), a divorcée, at the Adelaide Registry Office on 13 July 1921.
Their marriage was heavily affected by his wartime experiences.
In April 1922, a photograph of Jensen and his horse-drawn cart, with "J. C. Jensen V.C." painted on the side, was published on the front page of The Sunday Times newspaper in Sydney; the caption noted that he employed several men in his business.
On 28 May, Jensen was admitted to the Adelaide Hospital, and died of congestion of the lungs three days later, aged 31.

On 2 June, Jensen's casket was carried on a horse-drawn gun carriage to the West Terrace Cemetery, followed by hundreds of former members of the 50th Battalion, and he was buried with full military honours in the AIF section of the cemetery.
It was reported as "one of the most impressive funerals which have passed through the gates of the West Terrace Cemetery", and "probably one of the largest military funerals ever held in Adelaide".
The pastor at the service said that Jensen was, "modest always... ever ready to enlarge on the bravery of others, without touching on his own accomplishments".

Jensen's medal set, including his Victoria Cross, was donated by a family member to the Australian War Memorial in 1987 at a ceremony attended by Queen Margrethe II of Denmark, and is displayed in the Hall of Valour of the memorial.
In 2006, a memorial to Jensen was unveiled in Løgstør by the Australian ambassador to Denmark, and a book about him was published in Denmark in the same year.
Each year, wreaths are placed at the memorial in memory of Jensen, and in 2014 a wreath was placed by the Australian ambassador, Damien Miller.
After his discharge, Jensen worked for a short time as a barman in Truro, then as a marine store dealer in Adelaide. He married Katy Herman (née Arthur), a divorcée, at the Adelaide Registry Office on 13 July 1921. Their marriage was heavily affected by his wartime experiences. In April 1922, a photograph of Jensen and his horse-drawn cart, with "J. C. Jensen V.C." painted on the side, was published on the front page of The Sunday Times newspaper in Sydney; the caption noted that he employed several men in his business. On 28 May, Jensen was admitted to the Adelaide Hospital, and died of congestion of the lungs three days later, aged 31.
On 2 June, Jensen's casket was carried on a horse-drawn gun carriage to the West Terrace Cemetery, followed by hundreds of former members of the 50th Battalion, and he was buried with full military honours in the AIF section of the cemetery. It was reported as "one of the most impressive funerals which have passed through the gates of the West Terrace Cemetery", and "probably one of the largest military funerals ever held in Adelaide". The pastor at the service said that Jensen was, "modest always... ever ready to enlarge on the bravery of others, without touching on his own accomplishments". 
Jensen's medal set, including his Victoria Cross, was donated by a family member to the Australian War Memorial in 1987 at a ceremony attended by Queen Margrethe II of Denmark, and is displayed in the Hall of Valour of the memorial. In 2006, a memorial to Jensen was unveiled in Løgstør by the Australian ambassador to Denmark, and a book about him was published in Denmark in the same year. Each year, wreaths are placed at the memorial in memory of Jensen, and in 2014 a wreath was placed by the Australian ambassador, Damien Miller.
Jørgen Jensen (soldier)