The 21-year-old reigning European champion was named in the British squad despite tearing a posterior cruciate ligament in December.
However, the GB medical team has advised the Scot to regain full fitness before August's Olympic Games in Rio.
"Rehab has been going really well but we were running out of time," said technical director Shane Sutton.
"I'm disappointed for Katie and disappointed for the team but the [team pursuit] squad has a lot of depth so we're still confident we can show the crowds something special in London next week.
"Katie is a world-class rider and a key member of the Great Britain cycling team. We'll miss her in London but she'll be back stronger than ever and ready for Rio."
Women's sprint: Becky James, Katy Marchant, Jess Varnish.
Men's sprint: Matt Crampton, Phil Hindes, Jason Kenny, Callum Skinner.
Women's endurance: Elinor Barker, Ciara Horne, Emily Nelson, Joanna Rowsell Shand, Laura Trott.
Men's endurance: Steven Burke, Mark Cavendish, Ed Clancy, Jon Dibben, Owain Doull, Chris Latham, Andy Tennant, Sir Bradley Wiggins.
Katie Archibald will miss next week's Track World Championships in London because of a serious knee injury.