The bus, carrying schoolchildren aged five to 10, crashed at about 16:00 local time (21:00 GMT) on Monday.
Photos from the scene showed the bus wrapped around a tree, with its metal roof split in two.
"Speed is being investigated very very strongly as a factor in this crash," said Chattanooga police chief Fred Fletcher.
He said it was a complicated crime scene, but conditions "appeared to be clear and dry".
Investigators believe the bus may have hit a utility pole before colliding with the tree, the police chief added.
The driver, who survived the crash, was being questioned and was co-operating with investigators, police said.
A spokeswoman for the district attorney said five children were found dead on board the bus after the crash, and another child had died in hospital.
She said 35 children had been on board the bus. Chattanooga Fire Department also said 23 children had been taken to hospital by ambulance.
Local blood bank Blood Assurance called for blood donations following the crash.
A reporter for the local news channel tweeted that queues to donate were "out the door" and the office was taking appointments for the following morning.
The mayor of Chattanooga, Andy Berke, asked concerned parents to go to the elementary school for information, and not the crash site.
"Please pray for the families of those affected by this horrible accident," he said in a tweet.
At least six children have been killed and several others injured in a bus crash in Chattanooga, Tennessee.