The depiction, based on photographs of the couple at a sporting event, bears some resemblance to William but less so his fiancee.
Royal watchers said she appears much fuller in the face on the coin than she is in real life.
“This coin is of historical importance — to get it so wrong seems ridiculous,” Editor-in-Chief of Majesty magazine, Ingrid Seward, was quoted on the Sky News website as saying.
The design was approved by the 28-year-old couple and by William’s grandmother Queen Elizabeth.
The Royal Mint, which produced the collectors’ item, said it had no intention of changing the design.
“It is quite a subjective issue,” a spokesman for the Mint, based in Llantrisant, south Wales, told Reuters.
“It is always challenging to engrave profiles and features onto something as small as a coin, particularly the features of young people.”
Prince William, second-in-line to the throne after his father Prince Charles, announced his engagement to his long-term girlfriend in November, and the couple will marry on April 29.
The coin depicts him in profile — an allusion to his royal status — with Middleton looking at him face-on in a more informal pose, the Mint said.
It bears her full name, Catherine.
She is likely to become one of the most photographed women in the world, just like William’s mother, the late Princess Diana.
Production of the coin has yet to begin, and it is not clear how many will be struck, but orders have been taken.
The Royal Mint has created many commemorative medals and coins to mark special occasions, including the 2012 London Olympics as well as other royal events, but this is the first time it has created a commemorative royal engagement coin.
“The Royal Mint has been recording historical events for over 1,100 years and we’re fortunate to be in a role that allows us to add to that legacy,” Dave Knight, director of Commemorative Coin at the Royal Mint, said in a statement.
The coin comes in silver and gold, and its various models cost from 9.99 to 1,550 pounds ($2,400). Reuters