Neuner, a six-time world champion, came in second place just 1.5 seconds behind Slovakian surprise winner Anastastiya Kuzmina in the 7.5-kilometre sprint event.
She will have a second chance at gold on Tuesday, however, in the longer biathlon pursuit event. Competitors start in the order they finished in the sprint, with a handicap of the same time they finished behind the sprint winner, giving Neuner a strong chance to make up her time.
Neuner, 23, missed one target in the shooting and admitted after the event she had become tired towards the end. Nevertheless, she was delighted with the result.
“I'm proud of myself. The first medal for the German team, that's just awesome. I'm just trying to totally enjoy it and be pleased with myself.
“All of a sudden I was standing there and had this medal in my hand. And then I saw the flag, they played the national anthem and then I realised: I've really dreamed of this for years, since I was a kid. That is just a really huge dream that's been fulfilled.
“It's Olympic silver. For me that is just awesome. Besides, being 1.5 seconds short isn't much for the pursuit. So I know that the gold medal is within reach. I don't think you need to be sad about silver.”
German luge world champion Felix Loch also had a place on the dais firmly in sight after holding first place after two out of the four heats in the competition.
Ski jumper Michael Uhrmann failed to win a medal despite leading in the qualifying rounds after jumping 106 meters on Friday for a total score of 138.5 points. The gold in that event – the first of these games – went to Swiss jumper Simon Ammann.
The beginning of the games were marred by the death of 21-year-old Georgian luger Nodar Kumaritashvili, who crashed at high speed during training, leading to serious questions about the safety and preparation of the track.