The pair lost 12-16 to Russia's Vitalina Batsarashkina and Artem Chernousov who won the gold medal.
In a thrilling contest, Chaudhary and Manu fought back from 6-12 to make it 12 all. But the Russian pair held on to their nerves to walk away with the gold medal.
With Saturday's silver medal in the mixed team event, India now has three medals, two of them being bronze.
Russia is leading the field with seven medals, including three gold.
Chaudhary and Manu had topped the field in the first qualifying round, shooting 587 out of 600 after 60 shots (30 shots each team member).
But Abhishek Verma and Yashaswini Deswal, the second Indian pair in the fray, shot a combined 577, to finish fourth out of 32 teams.
Verma and Yashaswini lost to Iran's Javad Foroughi and Golnoush Sebgatolahi 7-17 in the bronze medal match.
In the 10m air rifle mixed team event, India's Elavenil Valarivan and Divyansh Singh Panwar finished sixth while Anjum Moudgil and Deepak Kumar finished 15th overall.
On Sunday, Manu and Rahi Sarnobat will be seen in action in the women's 25m pistol event. Sanjeev Rajput and Aishwary Pratap Singh Tomar will compete in the men's 50m rifle 3 positions event.
Osijek (Croatia), June 26
India's Manu Bhaker and Saurabh Chaudhary clinched silver in the 10 metres air pistol mixed team event at the International Shooting Sport Federation (ISSF) World Cup here on Saturday.
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