Children between the ages of five and 11 were aboard the bus, which flipped onto its side and slammed roof-first into the tree in Chattanooga, Tennessee.
Five youngsters are known to have died, with 24 more rushed to hospital, city police chief Fred Fletcher said.
"This is an absolute nightmare for this community," he said.
Local media reported how dazed children lay on stretchers at the scene of the crash, near Woodmore Elementary School, waiting for ambulances to take them to hospital.
Bus driver Johnthony Walker, 24, has been arrested, the police chief said. He was charged with five counts of vehicular homicide, reckless endangerment and reckless driving.
"Certainly speed is being investigated very, very strongly as a factor in this crash," Fletcher said.
"It was clear and dry... there did not appear to be any roadway conditions. But it is a complicated ... scene, it covers a significant area," he added.
Fletcher described the incident as "every public safety official's worst nightmare."
"But that is nothing in comparison to the nightmare that families, friends and our community is going through with this tragic loss."
Police do not have a list of all students who were on the bus, but at least 24 students were taken to area hospitals, Fletcher said.
The families of the five children confirmed dead had been notified. Information on the conditions of the nearly two dozen children at area hospitals was unavailable, Fletcher said.
"I hope as deeply and passionately as I can that there are no more, but I do not know the status of those kids," he said.
Amy Katcher, spokeswoman for Hamilton County Schools, told AFP that "this is the worst tragedy we have had to deal with."
"Heartbreaking school bus crash in Chattanooga," tweeted US Senator Bob Corker of Tennessee. "My thoughts and prayers are with the children, families and first responders."
Fletcher said a warrant was issued to remove the black box from the bus to review evidence.
The National Transportation Safety Board said on Twitter it would deploy a team Tuesday morning to investigate the crash.