Sodhi, who was considered as a bright medal prospect, failed to make the cut after a poor third round at the Royal Artillery Barracks.
India's lone medal, bronze so far, has been won by shooter Gagan Narang in 10m Air Rifle event.
However, another Indian shooter Vijay Kumar ended in fifth position in the first qualification stage of men's 25m Rapid Fire Pistol and has bright chances of making the final when the second stage of qualification is held on Friday. Vijay scored 293 points in the first qualification.
The 32-year-old was on his way to making the final line-up of six but his third round effort pushed him down the order and out of the Olympics.
After having started off with a score of 48 and adding a further 44 in the second, Sodhi experienced a slump in the third with just 42 out of 50.
Sodhi finished with a score of 134/150 to be in 11th position. The first place went to Great Britain's Peter Robert Russell Wilson with a score of 143.
Top six, who qualified for men's Double Trap final
1. Peter Robert Russell Wilson (Greta Britain) 143
2. Vasily Mosin (Russia) 140
3. Fehaid Aldeehani (Kuwait) 140
4. Vitaly Fokeev (Russia) 139
5. Hakan Dahlby (Sweden) 137
6. Richard Bognar (Hungary) 137
11. Ronjon Sodhi (India) 134