Members of the Communication Workers Union voted to strike in May in protest at Royal Mail's plans to close the office in Heanor.
The 25 staff would be transferred to Ilkeston, three miles (5.15 km) away.
But Royal Mail managers reassured people deliveries would not be badly affected during the strike and customers would receive their post.
Financial savings
"Our managers are working with us and people will be going in there to work nights," said East Midlands general manager Lynne Wilson.
"We'll also have people out on deliveries and will be manning the callers' office.
"So while it might take us a bit longer than it does our frontline colleagues - as clearly they do a great job - if customers do have any issues, they can ring the Heanor office as normal and we will do our best to help them," she said.
Royal Mail has previously said it needed to make financial savings. But the union disagreed, saying that closing the office would have an impact on the service provided.
The strike is due to end on Saturday.
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