The Dutch runner, who took gold over the distance at the 2024 Paris Games, picked up the injury while training on a treadmill.
Ethiopia-born Hassan, who won the 5000m and 10000m at the Tokyo Olympics, said pulling out of London had been a tough decision to make.
"To compete at that level, you need to be in perfect condition," said the 33-year-old, who won the London Marathon in 2023.
"After the incident, I hoped the injury would settle, but as training progressed, it became clear that I wasn't able to prepare at the level I expect from myself."
The 2026 race on the streets of the British capital takes place on April 26.