The health board said a “data error” caused 2,500 text messages to be sent to teenagers in Lothian inviting them for a second dose.
Currently, in line with national guidance, 16 and 17-year-olds in Scotland are only being offered one dose of the vaccines unless they are clinically extremely vulnerable themselves, living with someone who is, or are an unpaid carer.
The health board said on Friday it has sent a second text message urging the teenagers not to attend unless they fall into one of the above categories.
NHS Lothian is investigating the situation to establish what happened and how many letters have been sent via the national booking system to teenagers.
Pat Wynne, the health board’s nursing, primary and community care director said: “I would like to apologise to all of those teenagers affected and for any confusion and inconvenience caused.
“All of those who received a text message have been contacted again with more information on what to do next.
“We don’t yet know how many letters have been issued, but we are investigating fully to establish what happened and how many people are affected.