Katie and team-mates Laura Kenny, Elinor Barker and Elly Dickinson just lost out to Australia in a thrilling race for the gold medal after both quartets had posted the fastest times in qualifying.
The Australian four - Annette Edmondson, Ashlee Ankudinoff, Georgia Baker, and Amy Cure- started out the fastest, building up a lead of around three-quarters of a second as they powered round the velodrome in Pruszkow.
Britain came storming back in the closing stages as gaps began to appear between the Australian riders, but the Aussies held on to take gold.
The silver is 23rd major medal of Katie's career and she has now won six Worlds medals, including team pursuit gold in 2014 and silver in 2015 and 2018.
The 24-year-old is expected to look to add to that tally in Sunday's madison, while older brother John - taking part in his first World Championships - has high hopes in the individual pursuit on Friday.