Both Telford and Wrekin and Shropshire are in Tier 2 but neighbouring areas such as Wolverhampton and Staffordshire are in Tier 3.
Telford & Wrekin Council said it would be contacting would be customers to inform them that they will not be able to visit the venue under the current guidance.
The council said people living in Tier 3 areas should avoid travelling into the area other than for work, education, youth services, to receive medical treatment or because of caring responsibilities.
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A message on its website stated: "Under this government guidance people travelling from Tier 3 areas are asked to refrain from booking and attending any sessions or activities at Telford Ice Rink.
"We will contact any customers that try and book onto our sessions from Tier 3 areas to advise them that they will not be able to visit whilst restrictions remain in place in their local area.
"If you live in a Tier 3 area as per the government guidelines we ask that you do not book or travel to our facilities to help reduce the spread of coronavirus."