As Americans suffer through the worst influenza outbreak in almost a decade, a Japanese drugmaker says it has developed a pill that can kill the virus within a day. But even if the experimental drug lives up to the claim, it likely won’t be available in the U.S. until next year at the earliest.

A late-stage trial on Japanese and American flu patients found that for the people who took the Shionogi & Co. compound, the median time taken to wipe out the virus was 24 hours. That is much quicker than any other flu drug on the...