MMG said the accident happened in the Huallpachaca area of the Cotabambas province, which has a series of hairpin bends.
Local media reported the bus fell into a deep gorge.
The passengers were employees of contracting firms including Manpower, Geotec, MB Renting, AKD Drilling, Lavalin, M&RC, JRM and JP Natlian, MMG said.
"We express our deepest sorrow and grief and extend our sympathies and support to the family and friends of those involved in this tragic incident," the company said.
"Las Bambas is assisting search, rescue, police and medical treatment from Cusco and is offering direct support to the family members of those involved in the accident.
"Las Bambas is cooperating closely with local authorities in the investigation of the cause of the accident."
Las Bambas is the Hong Kong-listed company's flagship operation and produced 144,642 tonnes of copper in concentrate in the first half of 2021.
The company reported record first half net profit after tax of US$584 million, due in part to the sale of Las Bambas stockpiles after the operation suffered blockades and COVID-19 setbacks in the previous corresponding period.
MMG shares (HK: 1208) are trading near the middle of a one-year range, at HK$3.75 at the time of writing, capitalising it at HK$32.4 billion (US$4.2 billion).