Sharon Kemp, returning officer for Rotherham Borough, said: "Due to circumstances beyond our control, a small number of postal votes may have been delayed.
"We believe this could be up to one per cent of the overall number of postal votes.
"We are asking anyone who applied for a postal vote by the deadline of 5pm on April 20 and who has not received their postal vote with their post today to get in contact with us at [email protected] or call 01709 382121 as soon as they can.
"We will then deliver a replacement postal vote to those people.
"Once people do receive their votes, I advise them to move very quickly. Get the form filled in and return on the same day if possible.
"Voters have until Wednesday to put their vote in the post, they can also put their vote through the letterbox at Riverside House on any day up to and including polling day until 10pm or hand their postal vote in at any polling station by 10pm on polling day (Thursday, May 6).
It comes after Sheffield City Council revealed that 15,000 voters were yet to receive their postal votes last week due to a printing error.
The Guardian has contacted Bassetlaw District Council to find out if there have been similar issues with postal votes in Bassetlaw.