Staff are protesting against the decision and say the closure will mean they will have to give up work to care for their children.
The Child's Play nursery at Mount Pleasant, run by Kiddicare, opened in 1994 and is attended by up to 30 children.
Postal workers held a demonstration outside the nursery site in Clerkenwell to voice their opposition to the closure.
Delivery worker Angela McNaughton, who has worked at the site for 12 years, uses the nursery to care for her one-year-old daughter during her shifts.
She said, 'I'm a single parent and if I didn't have the nursery, I'd be forced out of employment.'
Mount Pleasant Communication Workers Union branch secretary Roger Charles said, 'This nursery is a hugely important resource for so many workers and its survival is crucial. It offers affordable childcare for shift workers, as it's open from 6am to 10pm. It's the only facility like it in Royal Mail and makes a huge difference to the lives of working families.
'We know that some people will have to resign if this nursery closes.'
The CWU said that postal workers are among London's lowest paid workforce, making subsidised childcare a vital asset for families.
Local MPs Emily Thornberry and Frank Dobson are supporting the campaign to keep the nursery open.
According to the Royal Mail, the nursery is being closed in November as a cost cutting measure. The Royal Mail informed parents of its decision at the end of last year.
A spokesperson said, 'Royal Mail has taken the difficult decision to close the creche at Mount Pleasant mail centre in November 2011, as the number of children using it is falling and Royal Mail currently subsidises the nursery at a cost of over £160,000 per year.
'Royal Mail gave the small number of parents affected one year's notice of its decision and is talking to them to see how it can help them make alternative arrangements.'