The health board said there has been instances of members of the public attending mass vaccination sites that are not yet open.
Covid-19 vaccinations are only available by appointment.
Dr Linda de Caestecker, public health director at the health board, said: “We share the public’s enthusiasm for the Covid-19 vaccination programme and understand people are very keen to get involved.
“We would like to ask the public to only attend a vaccination centre when you have been provided with an appointment. You will not be taken for an appointment if you do not have a booking.
“We also kindly ask for people to only arrive shortly before their appointment – there is no need to queue early. We need to maintain social distancing at all times and ensure there are no crowds.
“Thanks to everyone who has already taken up the opportunity to be vaccinated against Covid-19.
“Our vaccination teams are working through the priority groups and individuals will be contacted when it’s their turn for an appointment.
“We encourage everyone to do so when they are contacted.”
On the day of their appointment, patients are advised to bring their appointment letter with them and arrive as close to the appointment time as possible.
They must wear a face covering while travelling to and from their vaccination site, and during the appointment.
Anyone requiring assistance with travel to their appointment should contact the Traveline Scotland helpline on 0141 465 1878.