Plymouth City Council blamed the issue on a "computer problem" – but would not elaborate.
The blunder could stop large numbers of people from voting.
But a council spokesman confirmed 1,510 ballot packs did not make it to their destination and over 600 replacements have already frantically been been issued.
The issue has left some people – including students – furious and worried about not being able to vote.
Calls have been made for an urgent inquiry after 1,500 voters were left without postal ballots
In 2015, both Plymouth seats were won by Conservatives with a majority of less than 5 per cent.
Plymouth, Sutton and Devonport, won by just 523 votes, is one of the most marginal seats in the country.
Georgia Valentine, a 19-year-old Leeds University student from Plymouth, said: "I applied for a postal vote well within the deadline.
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"I was in the last batch of postal votes to be sent out, it was confirmed to have been sent last Wednesday first class, but I haven't received it and have now come to learn that there has been a batch lost by Royal Mail last week.
"I rang the council more than 20 times and got no answer. Now we are one day closer to the election, which I will not be able to vote in."
Plymouth University student James Hardy, 19, who travelled to Finland last week said: "It's been a complete and utter farce, I'm missing out on voting which is my democratic right through no fault of my own.
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The blunder could stop large numbers of people from voting
"It is completely and utterly unacceptable. I'm absolutely fuming with what has happened."
Council bosses in Plymouth, Devon, and Royal Mail were investigating the mix-up yesterday.
The cock-up means students, soldiers, sailors and anyone else who may live and work in the city temporarily, may not be able to place a vote.
Plymouth is a marginal "swing city" which could go either way on Thursday's election.
The council said: "We are still investigating the cause and will find out what happened and why.
"Our priority is to make sure that anyone affected can place their vote.
"We are issuing replacement postal vote packs to anyone who has contacted us to say they have not received one and have so far issued more than 600.
"On Tuesday evening and the first thing Wednesday morning we are delivering replacement postal vote packs to all those we have identified were missed out and have not yet contacted us."
They added: "We will continue to do everything possible to ensure people who applied to vote by post can do so."
The Royal Mail said: "Royal Mail takes its responsibility of delivering election information very seriously and is investigating this matter urgently."
The Electoral Commission said it was "satisfied with the steps being taken to rectify any problems".