One side of the £1 coin bears the image of Prince Philip and the phrase "Non sibi sed patriae", meaning "not for self, but country".
Prince Charles struck the coin during a visit to the Royal Mint in Llantrisant, Rhondda Cynon Taff, on Tuesday.
The silver and gold design has been approved by Prince Philip.
After his visit, Prince Charles, on the third day of his Welsh summer tour, was presented with the coin he had struck.
"Is that the one I made?" he asked. "I am very grateful."
The Royal Mint's chief engraver Gordon Summers said: "The image of the Duke of Edinburgh was taken from a prize medal from the 1970s.
"We are already working on a coin for Prince Charles' 70th birthday and I showed him the design for it.
"He asked what references we had used. We had a photography session with him about a year ago.
"We did not alter the image of his father, so his father looks younger than him on the coins."
The Royal Mint, which was first housed in the Tower of London, produces five billion coins each year for more than 60 countries.
Its headquarters in Llantrisant was officially opened by the Queen in 1968 in readiness for the introduction of decimal coinage.
The prince earlier met the Royal Welsh's regimental goat Shenkin III during a visit to the Regimental Museum of The Royal Welsh in Brecon.
The Prince of Wales has struck a commemorative coin to mark the Duke of Edinburgh's retirement from public duties.