This is an outdated belief that probably dates back to the 1800s. A fall, bruise or any other injury is almost never the cause of cancer. Sometimes a person might visit the doctor for an injury and find a tumour during consultation. The tumour is already present to begin with and not a result of the injury. People may also pay more attention to an injured part of their body, and some people discovered tumours while rubbing a painful area.
In some rare cases, long-standing and/or severe injuries can increase cancer risk. However, these account for only a small fraction of cancer cases. For example, skin cancer risk is somewhat increased in scars caused by thermal or chemical burns.