Muriel Robertson was the 7th child in a family of 12. The family was prosperous, and her father worked as an engineer and manager of a successful Glasgow firm. He died when Muriel was 16. She began an Arts course, but moved to science. She enjoyed scientific research, and spent some time examining parasites on leeches at the back of a fishmonger's shop in Rothesay. After graduation she travelled to Sri Lanka, and studied the parasites carried by tropical tortoises. In 1909 she began working at the Lister Institute of Preventive Medicine in London, where she spent the greater part of her career.
From 1911-1914, she was appointed by the Colonial Office to a temporary position in Uganda. There her job was to investigate the trypanosomes or parasites which infected tsetse flies, causing sleeping sickness, for which there was no cure. She succeeded in describing the life cycle of this trypanosome, and later microscopic techniques confirmed the accuracy of her work.
In the First World War, gas gangrene was a common cause of death among soldiers in the trenches. It was caused by the action of a type of anaerobic bacteria from the Clostridium family, which was present in soils. Muriel Robertson identified several species of Clostridium, and her work contributed towards later production of vaccines.