The 13-year-old made the podium in the boys’ B platform final in Russia.
McCabe had eased through the preliminary round, qualifying in third position, and he showed no nerves in the final to improve his score by more than 30 points.
The city youngster finished with 428.50 points, which was just 11.20 behind winner Oleksii Sereda of the Ukraine.
McCabe was the only competitor in the final with two dives scoring more than 70 points.
The medal caps a great year for the Plymouth teenager. He won a gold medal at the Dresden Youth International in April and picked up a synchro bronze medal at the British Diving Championships earlier this month.
McCabe’s medal follows on from fellow Plymouth diver Emily Martin winning a synchro gold with Andrea Spendolini-Sirieix on Wednesday evening.
Plymouth’s other competitor in Kazan, Aidan Heslop, will begin his campaign on Saturday when he competes in the three-metre synchro before taking part in the boys’ A platform event on Sunday.