Paramedics rushed the injured, who suffered neck pain or minor abrasions, to the hospital, Reuters reported.
Rex Auyeung Pak-kuen, chairman of MTR Corp., offered an apology.
“We will work together with the government to find out the truth as soon as possible so as to continue to provide safe services,” he said.
MTR Corp. has closed train stations, a target of vandalism during Hong Kong’s unrest, to stop protests. Train derailments in the region have been rare.
The protests were triggered in June by an extradition bill that many opponents saw as an example of China's increasing intrusion and at chipping away at Hong Kong residents' freedoms and rights, many of which have not been accorded to people in mainland China.
Hong Kong's government promised this month to withdraw the bill, which would have allowed some criminal suspects to be sent to mainland China for trial, but protesters have widened their demands to include direct elections for the city's leaders and police accountability.
More than 1,300 people have been arrested amid increasing clashes between protesters and police, whom demonstrators have accused of abuses.