But that figure is much higher during the Christmas rush when an extra 20,000 people, including thousands in Scotland, are hired under the contentious contracts, which do not guarantee work or pay
Labour criticised the large numbers involved, saying zero-hours contracts should "always be the exception not the rule".
Ian Murray, the Shadow Postal Affairs Minister, also questioned whether the number of the contracts would increase under the UK Government's plans to privatise Royal Mail.
But their use was defended by Royal Mail, which said the contracts gave the company much needed flexibility at busy times .
The figures were revealed in a letter from Moya Greene, Royal Mail's chief executive, to Labour MP Chris Ruane.
In it Ms Greene says that "at any given time during the year, on average, around 4900 of our workforce are on zero-hours contracts".
A spokesman for Royal Mail said those workers were employed through an agency. She added: "Royal Mail does not employ staff on zero-hours contracts, apart from during special events, such as Christmas, where we require short-term flexibility to handle greater volumes of mail."
Mr Murray said: "I would hope that Royal Mail would look closely at their use of zero-hours contracts during the Christmas period.
"While the company will undoubtedly need more staff during the hectic festive period, it could be argued that seasonal employee could be brought in on proper fixed term contracts. This provides certainty for families and individuals at an expensive time of the year, which will result in more committed and productive employees for Royal Mail."
There has been a public outcry over the contracts after it emerged this month there are one million zero-hours jobs in the UK, four times as many as previously thought.
The Scottish Government has suggested it could bar companies that use the terms from tendering for lucrative public procurement contracts.
Business Secretary Vince Cable has also launched a review of the practice and a report is due next month, but he ruled out banning the contracts, although he suggested they could need reform.
However, his proposals do not go far enough for a number of Labour MPs and trade unions who have called for a full-scale ban.
Labour this week highlighted claims by the Resolution Foundation think tank that the hourly wage for those on these contracts is about £6 less than other staff.
Unions have also warned the contracts exploit staff by offering no guarantees on work or wages.
They claim employees can also suffer through a system that makes it easy for individual managers to punish staff they do not like by withholding work.
However, business leaders have defended the contracts, saying they benefit many workers and employers and help to create jobs.
Across Scotland councils, universities and high-street names, such as McDonald's, have all admitted employing staff on the terms.