Five riders, aged between 19 and 22, were charged with driving while over the limit - and the sixth was charged with failing to provide a specimen.
Some residents have already complained that the project is a “free-for-all”, with people riding on the pavement, sharing lifts and using the 15mph machines irresponsibly.
Northumbria Police said seven people were arrested while using the e-scooters in the early hours of Thursday, with six of them subsequently charged with drink-driving offences.
All six will appear before North Tyneside Magistrates’ Court on March 25.
To hire an e-scooter, users must be over 18 and have a driving licence.
Operator Neuron welcomed feedback from local residents and, since launching the scheme, has put in an overnight curfew, blocking scooter hire between 11pm and 5am.
A spokesman said: “In the early days of a trial it is important to see how the e-scooters are being used and to understand what is working and what can be improved.
“We are working closely with Newcastle City Council and have already quickly adapted the service, and will be making further improvements to ensure that e-scooters can integrate into the city in the best, and safest, possible way.”
The scheme, which costs £1 to unlock a scooter and 18p per minute thereafter, allows them to be used in the city centre, Jesmond and Gosforth, which are popular student areas.
Earlier this week, Avril Deane, a retired newspaper columnist, said: “It’s a free-for-all at the moment.
“They are riding on the pavements, none of them are wearing helmets, we are all supposed to be socially-distancing but you see two people on a scooter.”