Police in Derbyshire said the driver was seen “jumping into the canal leaving his partner and 18-month-old baby in the car” following the crash.
A photo released on Twitter showed that the red Vauxhall Corsa, which was using false number plates, was badly damaged.
Detectives say the man was detained at the scene and remains in custody as an investigation gets under way.
The collision took place at about 2.10pm on Saturday in Long Eaton.
Although woman in the child in the Corsa were taken to hospital for checks, no one was seriously injured.
:: Witnesses or anyone with information can call police on 101, quoting incident 674.