Ireland's Data Protection Commission (DPC) says it "will examine Twitter's compliance with data-protection law in relation to that security issue".
Twitter has not commented on the claim.
The data is said to include phone numbers and emails, including those belonging to celebrities and politicians, but the purported size of the haul is not confirmed. Only a small "sample" has so far been made public.
While 235 million published records ranks among the largest breaches anywhere, it is only the latest in a stretch of security disasters at Twitter dating back more than a decade.
It would be worthwhile, at the very least, changing your password