The pair were beaten into second by Belgium's Lotte Kopecky and Jolien D'Hoore as the madison, raced over 30km for the women, made its championship debut.
The Belgians secured gold by winning the final sprint, giving them 45 points to Britain's 33.
With points awarded for the top four spots in the intermediate sprints, held every 10 laps, and double on offer at the end of the race, Australia's Amy Cure and Alexandra Manly claimed a battling bronze with a total of 26, despite a crash early on.
"I was nervous because we'd only ridden one each before, we didn't know what to expect," Barker, 22, told the BBC afterwards.
"I'm not surprised at all by the Belgians wining - they are a madison nation, so hats off to them, they were impressive."
It is Barker's second silver medal of the championships after the Welshwoman came second in the scratch race.
Britain lie joint third in medal table with a gold, two silvers and a bronze.
Read the original article on Eurosport: British women claim madison silver behind dominant Belgium