WASHINGTON — The world’s first vaccine against the leading cause of childhood diarrhea — a virus that hospitalizes 55,000 American children each year and kills 1 million in other countries — won Food and Drug Administration approval Monday.

Widespread vaccination with RotaShield could prevent 1 million American preschoolers every year from getting diarrhea caused by the intestinal infection rotavirus and keep 34,000 of them out of the hospital, said manufacturer Wyeth-Ayerst Laboratories, which is selling the vaccine created by the National Institutes of Health.

Good health care limits rotavirus-caused deaths in this country to no more than 40 a year, so the drug’s biggest U.S. impact will be in preventing severe illness and the resulting $400 million in medical bills.

But in developing countries where rotavirus is less easily treated, experts say the vaccine could save thousands of children’s lives — if other countries also approve the drug and can afford to buy it.

“The thing that will probably limit its use in developing countries, unfortunately, may be cost,” said Dr. Karen Goldenthal, FDA’s vaccine director. “It’s got to be incredibly cheap to be implemented.”

Wyeth will sell RotaShield for $38 a dose in the United States; children would swallow three doses, at ages 2 months, 4 months and 6 months.

The company declined comment on how much it would charge in poorer countries.

But the NIH scientist who discovered the drug said Wyeth officials have promised him they’ll somehow get the vaccine to children in developing countries, probably by using profits from rich countries to subsidize poor ones.

“It’s very exciting news today,” said Dr. Albert Kapikian, who has worked toward a vaccine for 24 years. “I think it’s going to have a major impact.”

Rotavirus is the leading cause of severe childhood diarrhea, attacking the lining of the small intestine.