The 18-year-old is bidding to become the first player since 1930 to successfully defend the Boys' Amateur title in a year when he has also won both the Scottish Boys' strokeplay and matchplay events.
Ferguson had earlier faced a stiffer task against England's Oliver Clarke in the third round, with the Scots youngster needing a birdie on the 18th hole to win by one.
He made short work of his afternoon match, sending Schmitt home after 11 holes. Afterwards Ferguson said: "From the word go I was hitting it awesome all day. I have been trying to hit the ball the best I possibly can on the one shot that I'm standing over instead of getting ahead of myself.
"I hit a lot of long irons really close to the hole, which made it hard for Max to play well because I was putting so much pressure on him. I don't think he gave the match to me, I just think I played really well on the day. On another day he could have beaten me."
Ferguson will now face 17-year-old Lewis George, of England, who defeated Denmark's Morten Toft Hansen 4&3 in their quarter-final.
Sweden's Oskar Bergqvist continued to impress yesterday, producing a bogey-free round to beat Norway's Jarand Arnoy 4&3 in the third round, then securing a 5&3 win over England's Billy Watson. He'll play Norway's Christoffer Bring in the quarter-finals.
Ireland's Rowan Lester was a 3&2 winner over Matthew Myers of England, while Tim Harry of Wales won by the same margin against England's Louis Lazarus. Bradley Moore defeated his fellow English international Jamie Li by two holes.