The study adds to the growing body of evidence that having too much iron is almost as bad as having too little.
High iron levels are also linked to a greater heart attack risk.
The researchers from the Hospital Universitari in Girona, Spain, believe that the iron might combine with chemicals to damage cells. This process is known as oxidative stress.
Lead researcher Dr Antoni Davalos said: "High body iron stores might contribute to stroke progression by increasing the production of free radicals in brain cells and in the walls of brain microvessels.
"Free radicals destroy the cell components and promote other mechanisms of injury that might enlarge the damaged area of the brain."
Dr Davalos and his team checked levels of ferritin, which is an indicator of iron content, in blood samples taken from 100 stroke patients.
Of these patients, 45 had signs of progressive brain damage such as slurred speech, and they had much higher average ferritin levels.
Dr Davalos, writing in the journal Neurology, said some people had a natural tendency to higher iron levels.
Stored iron
He said: "Stored iron increases with age in normal people, but iron accumulation is accelerated among a small percentage of the population.
"For these people a diet low in iron should be recommended.
Blood ferritin levels should be tested as we test cholesterol or glucose levels in patients with cardiovascular diseases or cardiovascular risk factors."
The main source of iron for most people is red meat.
Other researchers have found that men who regularly donate blood have a lower risk of heart attack, and they have speculated that it is because giving blood helps deplete iron levels.
Some researchers also believe that one reason premenopausal women have a lower risk of heart attack is because of their regular monthly blood loss.