Migraines affect some 12% of the population
An estimated one in 10 "migraineurs" suffer from a form of the condition which involves "aura" as well as the better-known headache attacks.
The "aura", which normally happens an hour or so before the headache, involves various kinds of sensory disturbance, such as dizziness or vision changes.
A team of geneticists from the University of California in Los Angeles looked at blood samples from the members of 50 Finnish families which each had three or more sufferers.
They looked to see if any of the families had genetic markers in common.
In 30% of the 430 people studied, the scientists found three common genetic markers linked to one particular part of chromosome 4.
Their findings were published in the American Journal of Clinical Genetics.
Dr Aarno Palotie, the lead researcher, said: "For the first time, we have proof of an isolated genetic link to migraine.
"This finding moves us one step closer to isolating the gene that predisposes people to migraine headache with aura."
He now plans further research to try to pin down particular genes connected with the condition.
Dr Andy Dowson, director of the Headache Service at King's Healthcare Trust in south London, said: "We already know that there are genetic factors involved in migraine.
"We know that if one or both parents has migraine, the chances of their children developing migraine go up.
"This research is interesting - it adds another piece to the jigsaw."
He said that if the finding eventually led to a target for therapies, then that would be a substantial find.
This is not the first genetic discovery about migraine - in 1997, a team of Dutch researchers identified a gene involved in a rare form of migraine called familial hemiplegic migraine.