The MTR said it had been informed of the decision by mainland railway authorities.
The cancellations come amid a high alert on the mainland as Typhoon Bavi approaches.
The typhoon is forecast to make landfall over the coast of southern Zhejiang in the early hours of Sunday, according to the National Meteorological Centre.
The agency has issued an orange alert, the second-highest level in the mainland’s four-tier weather warning system, indicating gales and heavy rain are in the offing.
The cancelled train trips on Saturday include five departing from West Kowloon Station for Shanghai Hongqiao, Fuzhou and Guangzhounan stations, as well as five in the other direction.
Eight more train services involving the same stations will be cancelled on Sunday.
The MTR called on passengers to check the latest train schedules on the mainland’s railway ticketing website and its associated app.
It said ticket refunds can be processed online and that there is no need to go to the station.
