National news agency Bernama reported that seven of the injured were in serious condition.
The accident occurred at 4:45am on the North-South Expressway, which runs the length of the country from the Thai border in the north to Johor Bahru at the tip of the Malaysian peninsula in the south.
Bukit Gantang, in the state of Perak, is about 200km north of Kuala Lumpur.
Bernama said the bus - travelling from Johor Bahru to the northern town of Alor Star - was going downhill when it hit the curb and careered off the road for 20 metres before flipping over and landing on its side in a five-metre-deep ditch.