Members of Walsall Local Outbreak Engagement Board said anti-vaxxers and anti-maskers were "not helping the cause" as the town prepares for the possible roll out.
It is hoped the first doses of the vaccine will be ready to administer to the most vulnerable before Christmas following developments by pharmaceutical corporation Pfizer.
But Dr Anand Rischie, chairman of Walsall Clinical Commissioning Group, said he was "disheartened" by claims he was seeing on his social media pages.
He said: "We are very strong believers in science and we will wait for the paper and peer review before we can even convince patients to take on this.
"But there is a good indication that preparation for December and this side of Christmas to protect our most vulnerable.
"My biggest issue is around fake news. How fake news is swarming all over Twitter and some groups that are anti-vaccine and they are spreading their message out.
"As soon as we get some evidence we will need to put FAQs on local websites to direct people where they can get those right answers rather than believing anywhere else.
"It’s very disheartening to see that fake news coming up on to my feed at the moment."
Board chairman Stephen Craddock added: "Yes, there are the anti-vaxxers and anti-mask wearers as well, both of whom are not helping the cause at all."
Walsall’s director of public health Stephen Gunther said they were planning for a roll out and that both the NHS and local authority would be ready once a vaccine becomes available.
He said: "Obviously, these are early days and obviously a few more hoops to jump through.
"We are looking to roll out and be ready for when it comes. We’re getting our plans ready and making sure we are able to mobilize as and when the vaccination comes. It’s a partnership with the NHS very much leading it with local authority support.
"We’re planning for December but in terms of when, we’ll have it when it’s ready and its not for me to pre-empt when the pharmaceutical companies have gone through all the rigorous safety checks which they do.
"My advice is to support the vaccination and make sure you are having it if you are eligible. We are gearing up to roll it out in the coming weeks if not months, depending on when it arrives. But please bear with us."
Councillor Craddock added: "Even if we start in December, the vast majority will be next year. The priority is the higher risk groups who will take the first dosages that are available."