Al Deehani, 33, made a run at Britain's Richard Faulds and Australia's Russell Mark over the final shots, but he came up short 186 to 187.
He finished a single point behind rivals from Britain and Australia.
"I am very happy to win Kuwait's first ever Olympic medal," said Al-Deehani, who is competing in the Olympics for the third time.
It was also the first Arab medal of the Sydney Games five days into the 16-day long event.
Stiff competition
Al Deehani, 33, made a run at Britain's Richard Faulds and Australia's Russell Mark over the final shots, but he came up short 186 to 187.
Faulds, 23, took the gold in a shoot-off, beating Russell to second place.
Al Deehani's medal comes 26 years after Kuwait first took part in the Olympics.
Al-Deehani's progress
Al-Deehani who comes from a family steeped in the traditions of hunting, was voted Asian athlete of the year in 1994.
He finished sixth in the 1998 double trap world championships in Barcelona and won a bronze medal in the same event the following year in Tampere, Finland.
The army officer won the New Delhi leg of the World Shotgun Cup in the double trap this year.
Prior to Sydney, the best Kuwaiti performance came in the 1992 Barcelona Olympics when they lifted a bronze in taekwondo, but it was only a demonstration sport at the time.
At the 1980 Moscow Games, the then Asian Champions, Kuwait, reached the quarter-finals before crashing out.
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