The herbal remedy, available in health food shops and some pharmacies in the UK, is used in China to aid memory and fight depression.
In a trial of 330 stroke patients over six months in China, the supplement was linked with better cognitive skill scores on tests.
Experts say the evidence for ginkgo is too weak to recommend it.
Those behind the small study - published in the online journal Stroke & Vascular Neurology - admit that larger, longer and more robust trials are needed.
It was carried out by Nanjing University Medical School, with patients from five Chinese hospitals.
All 330 participants began the trial within a week of having an ischaemic stroke. The average age of the patients was 64.
Roughly half of them were given 450mg of ginkgo biloba daily, in addition to 100mg of aspirin, while the remainder were given only the aspirin.
During a stroke, the blood supplying vital parts of the brain is interrupted, often leading to impaired memory and a decline in organisational and reasoning skills among stroke survivors.
Researchers wanted to see if combining ginkgo biloba with aspirin might help lessen or halt the cognitive decline.
Previous experimental studies in animals have suggested that ginkgo biloba protects against the nerve cell death associated with blood clots in the brain, possibly by increasing blood flow in the cerebral arteries.
Strokes - the definitions
Transient ischaemic attacks (also known as mini-strokes) - symptoms resolve within 24 hours but the majority resolve within 10-60 minutes.
Minor stroke - symptoms last more than 24 hours but often resolve within a few days - and are usually relatively mild
Major stroke - usually taken to mean some permanent symptoms remain
All the participants took a neuropsychological test (Montreal Cognitive Assessment) at the start of the trial, and then 12, 30, 90 and 180 days later, to check for any cognitive impairment.
The results showed that those taking the combination of aspirin and ginkgo biloba had higher scores for cognitive skills, including memory and reasoning, then those who weren't.
Speech problems and muscle strength also improved more rapidly, with indications of improved functional capacity 12 and 30 days after the start of treatment. However, both the clinicians and the patients knew which treatment they had been assigned to, which may have skewed the results, and the monitoring period was not very long.
Ginkgo biloba is one of the oldest living tree species.
Researchers say the extract used in the study contained more protective, and fewer harmful, chemicals than the extract typically used in previous studies.
Few side-effects were reported during the trial.
The participants were subsequently monitored for nearly two years, with little difference in the vascular health of the two groups: 16 people in the combined treatment group, and 20 in the aspirin group had further problems, including recurrent stroke and aneurysm.
However, longer term studies looking at stroke severity are necessary, before any more definitive conclusions can be reached.
Dr David Reynolds, Chief Scientific Officer of Alzheimer's Research UK, criticised the methodology used in the trial: "The researchers were able to tell which participants received the ginkgo biloba extract and which didn't - a set up that can strongly influence results.
"There have been extensive trials investigating the effects of this herbal extract in people with dementia and they have not shown convincing evidence of a benefit."