Department for Transport figures, published for the first time, show five casualties were recorded by South Yorkshire Police as having been involved in accidents with the vehicles in 2020.
Across Britain, police forces recorded 484 casualties resulting from 460 e-scooter incidents last year.
Of the casualties, the majority – 384 – were e-scooter riders.
It is currently illegal to ride e-scooters on public roads outside of Government-backed trials, which began in certain areas last summer.
The DfT said the figures are likely to relate largely to private use.
One person – an e-scooter rider – was killed and 128 people were seriously injured following crashes across Britain last year.
The DfT warned many non-fatal casualties may have gone unrecorded nationally because there is no obligation to report such incidents to police forces.
Trials for the use of the vehicles, which are similar to conventional kick scooters but powered by an electric motor and battery, started in July 2020 and are currently active across 31 areas in England.
However, the figures do not distinguish between incidents involving privately-owned e-scooters and rental ones.
David Renard, transport spokesman for the Local Government Association, which represents councils, said: “The use of e-scooters on public highways and footpaths outside of designated trial areas is illegal.
“Councils and operators are working together in these trial areas to ensure that routes are safe for both users and other members of the public and thereby reduce the chance of injuries.”
The Government said ministers had recently written to all major e-scooter retailers reminding them of their responsibility to inform customers of the law when selling e-scooters.
Excluding e-scooter riders, pedestrians and cyclists were the main other road users involved in crashes with the vehicles across Britain last year.
There were 57 pedestrians injured – 13 seriously – and 21 cyclists, with a third reporting serious injuries.
The figures show 22 vehicle occupants, including cars, vans and a bus, were also listed among the victims.
The majority of casualties whose age is known were at least 40 years old, including nine in the 70 and above category.
Eight children under 10 were also injured.
Of the e-scooter riders who were injured following crashes, around two-thirds were aged under 30, including 118 who were 10 to19 years old and two who were under 10.
Some older e-scooter riders were also among the casualties, including one who was at least 70.
A DfT spokesman added: “Safety will always be our top priority and the trials currently taking place in 31 regions across England are allowing us to better understand the benefits of e-scooters and their impact on public space.
“Evidence from the trials will allow government to consider how best to design future regulations and avoid the issues that other countries have faced.“
Anyone wanting to report details of any collisions involving e-scooters in South Yorkshire can report incidents to South Yorkshire Police on 101.