Panwar won the second stage competition, totaling 20 minutes and 35.87 seconds Monday night, but finished second overall.
In a new format, there is no final in athletics (with the exception of the 4 km cross-country) at the Youth Olympic Games and each event takes place twice, the results of both counting innings for the final ranking.
Panwar, 17, was second in the first stage in 20.23.30 seconds, behind Oscar's Patin from Ecuador.
Oscar, who finished second in the second leg, won the gold medal clocking 20: 13.69 and 20: 38.17.
The total Panwar time of 40: 59.17 was more than seven minutes slower than that of Oscar 40: 51.86. Jan Moreu of Puerto Rico was third to win the bronze medal.
It is India's first athletics medal in this edition and the third overall. Arjun (men's discus) and Durgesh Kumar (400m hurdles) each won a silver medal at the first edition in 2010.
"It's a great feeling, I'm very happy to have won a medal, I've done a lot of work for the Games, it's my first medal for India," he said. said Panwar after winning the silver medal.
"My next goal is to improve my performance here and to win a medal at the senior level as well," he added.