The programme, which began in September, will see the most vulnerable groups offered a third dose.
The Scottish Government initially announced that over 50s, unpaid carers and those with underlying health conditions would be able to book their third dose online from October.
However, this appears to have been delayed, with the NHS Inform website now saying over 50s can book this from “mid November”.
Liberal Democrat leader Alex Cole-Hamilton accused the government of “sneaking out” this delay, and said the health secretary must engage with the public.
"The Scottish Government are sneaking out changes to the vaccination program under the radar," he said.
"We know that caseloads are still far too high so there can be no excuses for these delays. The Health Secretary needs to tell the public what steps he will take to speed up this rollout.”
Scottish Conservative Shadow Health Secretary Dr Sandesh Gulhane accused the government of “sneakily shifting the goalposts on their own vaccination timelines".
“These documents show how they have quietly dropped their initial targets,” he said.
“When the SNP should be quickening the pace of the vaccine booster jag scheme at every turn, instead they are slowing it down.
“Humza Yousaf needs to urgently step up his game and guarantee jags will be in the arms of those eligible as soon as possible.”
The Scottish Government’s initial announcement on the Covid-19 booster programme stated: “Adults aged 70 years and over and those 16 years and over who are on the highest risk list (previously known as the shielding list) will begin to be contacted by letter or by their GP from the end of September…. Other eligible groups - including all those aged 16 to 49 years with underlying health conditions, adult carers, unpaid and young carers, adult household contacts of immunosuppressed individuals and all adults over 50 - will be able to book an appointment online from October.”
Mr Cole-Hamilton added that he is concerned about “errors” in both the Covid-19 booster and the flu vaccination campaigns.
It comes as Scottish Labour public health spokesperson Paul O’Kane wrote to Humza Yousaf urging him to “sort out” the flu vaccine programme.
He said he had heard from a number of constituents asked to travel long distances to receive their jag, many of whom were elderly or with health issues, and were concerned about a lack of public transport.
“If we are to avoid deepening this crisis further, then we need to see a swift, efficient and successful rollout of the flu vaccination and the booster programme,” Mr O’Kane said.
“But evidence from constituents has revealed that many, including the elderly and the disabled, are being asked to travel tens of miles to be treated.
“This is inefficient, unworkable and, with winter looming, potentially dangerous.
“That’s why the Health Secretary must act and act fast to ensure that people get the vaccinations that they need at a place that it is safe and accessible.”