Fabienne Hase and Volodin topped Sunday's short programme with 80.01 points, their clean execution allowing them to capitalise on the mistakes of their rivals.
But their overall total of 219.09 left them well short of Japanese champions Riku Miura and Ryuichi Kihara's winning score of 231.24. While the Miura and Kihara recovered from a disappointing short programme to grab gold with an awe-inspiring free skate, Georgia's Anastasiia Metelkina and Luka Berulava claimed silver with 221.75.
"It doesn't suck at all, to be honest. It's a medal at the Olympics. I think it doesn't matter which colour," Fabienne Hase told reporters.
"We can bring home a bronze medal from our first Olympics together. I think that's pretty amazing."
"A lot of people said we should get gold, but I think we're (just) as proud to bring home bronze for figure skating," the 26-year-old added.
The 2025 world silver medallists have been skating together since 2022.
St Petersburg-born Volodin, who previously represented Russia, was able to compete at these Games after he was granted German citizenship last year. The change of country revived his career, which had stalled in Russia.
Fabienne Hase and her previous partner, Nolan Seegert, were forced to withdraw from the team event at the Beijing Olympics after Seegert tested positive for COVID-19.
With Seegert in quarantine, Fabienne Hase trained alone for 10 days, and they eventually finished in 16th place in the pairs competition.
German figure skaters have struggled to shine in recent years, with Fabienne Hase and Volodin standing out as the country's only medal prospects in the sport at the Milan Games.
The country last won an Olympic figure skating medal in 2018, when Aljona Savchenko and Bruno Massot won gold in the pairs event at PyeongChang.
"The arena was loud, we had tons of German flags, German fans in the stands; we hadn't expected anything like this ... something huge," Fabienne Hase said.
"I'm still incredibly happy that we were able to give all the spectators who came especially for us this moment on the podium, and that we could celebrate together in this beautiful arena."