The error concerns postal ballots sent to what the council said is a "small proportion" of voters in the Much Wenlock area.
Instead of containing the list of local candidates, the paper instead included the list of those contesting a ward in the Market Drayton area.
Shropshire Council said "the wrong ballot paper had been included by the printers".
Robert Padfield, 73, of Broseley, who had one of the incorrect ballots, said that it could be confusing for those who have received them.
He said: "It is very concerning that Shropshire Council don't check things when they are sending out ballot papers. That's ridiculous.
"It was just confusing. To think the only option we had was someone from Market Drayton for that Much Wenlock ward. I thought maybe they had changed the boundaries.
"I can imagine some older people might not have queried it.
"There is no doubt about it - there will be people who have been confused by it."
Shropshire Council said that people would not be able to use the ballots because they have been cancelled.
A spokesman for the authority said that those affected would have new ballots sent out with letters explaining what had happened.
He said: “We can confirm there was an issue with postal ballot paper packs that have gone to a small proportion of electors in the Much Wenlock Unitary Division, where the wrong ballot paper had been included by the printers.
“We have cancelled these and new ballot papers are being issued to them tomorrow and a letter is being enclosed to explain the situation.”
The development comes ahead of next month's election, which covers all seats on Shropshire Council.
The poll will see 232 candidates vying to be elected to one of the 74 positions on the council.
Taking place on May 6, the election will be slightly different with some distancing and Covid regulations meaning minor changes to the normal polling station feel – people will be asked to take their own pens, and will have to fill out their ballot while wearing a face mask.