Only 150 of the bronze commemorative "coins" will be struck at Llantrisant site in Rhondda Cynon Taf, with all 57 Newport schools also being given one each as a memento.
One side features a map of Wales, the other side has the Nato summit logo.
It is not officially a coin as it does not have the Queen's head on it, so is not legal tender.
Wales Office Minister Baroness Randerson said: "It is a great way to help mark the biggest gathering of world leaders the UK has ever hosted".
She will join the deputy mayor and mayoress of Newport to see the striking of the final piece on Wednesday.
Each piece is 63mm in diameter and was designed by the Royal Mint's engraver Jody Clark.
It features the Nato logo and the words 'Nato Summit Wales 2014' in English and Welsh.
Shane Bissett, the Mint's director of commemorative coin, medals and bullion, added: "It is our great honour to have the opportunity to mark this year's Nato Wales 2014 Summit in this way, and leave the world leaders with a lasting reminder of their visit to Wales."
The summit will take place on 4-5 September.
US President Barack Obama, German Chancellor Angela Merkel and French President Francois Hollande are expected to attend along with leaders and senior ministers from around 60 other countries.
The Royal Mint has created a limited edition piece for world leaders at September's Nato summit in Newport.