The safer neighbourhood team for Broseley and Much Wenlock said that people have complained of "disgraceful" anti-social behaviour in the area, and that those going out to harass elderly or vulnerable people could be fined for breaking lockdown rules.
A statement on social media which has since been deleted said: "There have been two reports of snowballs being thrown last night between 11 and 11.30pm.
"This is obviously not a justifiable reason to be out of your house, this behaviour is likely to result in a £200 Fixed Penalty Notice for breaking the lockdown rules."
West Mercia Police later said that the initial statement did not provide the full context.
Superintendent for the Shropshire area, Mo Lansdale, said: “This morning one of our local teams tweeted about a number of incidents where snowballs were being thrown at the homes of elderly and vulnerable residents at gone 11pm.
“We fully appreciate that from their initial tweet it is difficult to get the full picture, and context can be tricky to gain in just 280 characters. They followed up with a tweet with more detail a few hours later and we’ve deleted the original post, to avoid any confusion.
“In relation to last night’s incidents we are speaking to a number of people to identify who the three individuals involved were. At this time, no one has been spoken to or issued with a fixed penalty notice.
“The pandemic is stressful enough for people, particularly those that are more vulnerable, without them being made to feel worse and isolated in their own homes as a result of disgraceful anti-social behaviour.
“We will not tolerate the targeting of vulnerable people and there are a number of powers available to us to protect people. One such power could be the FPN under the Covid-19 regulations as, I think we can all agree, frightening vulnerable people is not a reasonable excuse to have left your home.”
Earlier police in Broseley said fines had been issued in the town for "blatant" breaches of coronavirus lockdown restrictions.
Learn more about the third English coronavirus lockdown at gov.uk/guidance/national-lockdown-stay-at-home.