It comes after West Mercia chief constable Anthony Bangham said rules will be 'strictly enforced' following the tightening of coronavirus restrictions and the implementation of harsher fines.
Not wearing a face mask without reasonable excuse now carries a £200 fine for a first offence.
Shrewsbury Police said: "Two tickets given for two males not wearing a face mask whilst in a store without a reasonable excuse.
"The law is the law, we need to keep ourselves and each other safe."
Mr Bangham said last week: "The new restrictions outlined in law by the Government are designed to limit the spread of the infection, save lives and hopefully prevent the need for further and more significant regulations in the future.
“Throughout the Covid-19 pandemic West Mercia Police has engaged with communities, keeping enforcement action to a minimum wherever possible, and the majority of people have behaved sensibly and responsibly.
“However, increasing infection rates demonstrate that there are people who are choosing to break the law and they are putting people at risk as a direct result of their actions.
“Therefore, I want to make clear that anyone who chooses to ignore the regulations and restrictions can expect strict enforcement from West Mercia Police and to be given a fine."