The four-time Olympic champion crashed while racing in the Tempo round of the women’s Omnium at the World Cup in Milton on January 26.
Kenny consulted with a surgeon directly following the accident who told her that the Tokyo Olympic Games was "off the cards", according to her interview with the BBC.
"I told him, 'An operation's not for me, thanks'," she told the BBC. "Did I want an operation to get it fixed, but with a two-week delay in me getting back on the bike, or did I want to just see how it goes? I decided to see how it goes and the next day I got back on my bike."
Kenny will compete in both the Omnium and Scratch Race at the World Championships but will have to forgo the Madison and the Team Pursuit.
She is also aiming to defend her titles in the Team Pursuit and the Omnium, and compete in the Madison at the Tokyo Olympic Games held from July 26 through August 9.
"I wanted to put my hand up for all three events in Berlin but I can't physically do the Madison and I can't do a standing start in the Team Pursuit," Kenny told the BBC. "That's slightly frustrating but I never thought I wouldn't go to the Worlds and I know a lot of people within British Cycling thought I'd lost the plot.
"If I have the form that I had a month ago, I'd like to think I could still get selected for all three events come Tokyo."
Kenny won Olympic gold medals in the Team Pursuit and Omnium in 2012 in London and in 2016 in Rio. She is also a seven-time world champion on the track as a member of Team Great Britain.
She took some time off following her pregnancy and birth of her first child, Albie, and returned to racing at the 2018 UCI Track World Championships.
"I haven't sacrificed all this time with him for no reason, and a part of me was thinking that when I crashed, I haven't put in all this hard work and had all this time away for no reason, so there was no way I was not going to the Worlds.
"I do it for Albie now. I want him and everyone to be able to see that these little hiccups happen but why should they get in the way? I know it's a broken bone, I'm not stupid, but if I can ride I will ride," she told the BBC.