Hurricane-like winds left about 1 million households and businesses without electricity Monday as schools closed and rush-hour commuters faced obstacle courses of fallen trees and intersections without working traffic signals.

Sunday’s wind storm caused by remnants of Hurricane Ike killed at least three people who were hit by toppled trees, authorities said. It could take a week for power to be restored in some areas.

Winds gusting up to 78 mph ripped roofs from buildings and blocked roadways across the state, with southwest and central Ohio bearing the brunt of the storm’s force, according to the National Weather Service.

‘‘What we experienced was a hurricane-force wind gust,’’ said meteorologist Myron Padgett at the National Weather Service in Wilmington.

A falling tree killed two motorcyclists in Hueston Woods State Park in southwest Ohio, and a woman died in the Cincinnati suburb of Mt. Healthy when a tree fell through the roof of her home.

As of 8 a.m. Monday, 575,000 Duke Energy customers in southwest Ohio and northern Kentucky still had no power, out of 867,000 who had lost service since the storm began to hit the region late Sunday morning. It was the biggest outage in the company’s history, said Duke Energy spokeswoman Kathy Meinke.

American Electric Power said on its Web site Monday that about 539,000 of its Ohio customers, or 37 percent, were out, including 273,000 in Franklin County, which includes Columbus.

In Lawrence County, as of Monday morning there remained 222 American Electric Power customers without power.

That is less than one percent of the number of customers serviced by AEP.

The Ohio State Highway Patrol reported no accidents because of the wind, but a tree was blown across the intersection of County Roads 6 and 52.

By 7:30 this morning crews had removed the tree and the roads were reopened.