Stewart was originally expected to walk the red carpet but has "pulled out" of the premiere because she is "too ashamed" to make any public appearances right now, reports Radar Online.
"After everything that has been said, and in light of the revelations that she cheated on Robert with director Rupert Sanders, she's running scared at the moment," a source claimed.
It was revealed last month that Stewart cheated on boyfriend Robert Pattinson with her Snow White and the Huntsman director Rupert Sanders, who is married to model and actress Liberty Ross.
Stewart apparently also decided not to attend the London premiere because she wants to avoid awkwardness, since Pattinson's close friend Tom Sturridge is scheduled to make an appearance at the premiere.
"He's very close to Rob and Kristen thinks it would be awkward for her to promote the movie on the red carpet alongside him," the source explained.
[Kristen Stewart in a still from 'On the Road']
"Kristen is very proud of her work for On The Road. She grew up reading Kerouac novels, and this is a production she always wanted to star in. If she appears at the London premiere, it will detract people from the movie itself and Kristen doesn't want that at all.
"She wants her performance and this film to be recognised for what it is – a great adaptation of a classic book."
On The Road is a big screen adaptation of Jack Kerouac's 1957 Beat Generation novel about two friends who take a roadtrip across the US.
Its star-studded cast includes Garrett Hedlund, Sam Riley, Amy Adams, Kirsten Dunst and Viggo Mortensen.
Watch a trailer for On The Road below: