The company, Voi - who also stopped the scooters being used on Christmas Eve until the morning of Christmas Day - have said they will disable them from 9pm on 31 December to 8am on 1 January.
The scooters have become a popular mode of transport for people in Bristol since they were introduced as part of a trial in October 2020.
However, safety concerns about them have also been growing, with one recent study revealing that 90 people were injured as a result of e-scooters in the city in just one four-week period.
The data - which was compiled as part of a study from by the Parliamentary Advisory Council for Transport Safety (PACTS) - said that e-scooter riders were left with fractured limbs and head injuries - with three patients suffering a severe traumatic brain injury.
Around 2.5 million trips have been taken on the scooters in Bristol, Bath and South Gloucestershire since the start of their trial in October 2020.
The trial is one of about a dozen taking place across the country which are being coordinated by the government, who want to see how safe they are.