He reached the final of the 2012 Amateur Championship at Royal Troon Golf Club, losing to Alan Dunbar by 1 hole.

Schwab turned professional in June 2017 and played on the Challenge Tour for the rest of the year, finishing 33rd in the Order of Merit.

He tied for fourth place in the Hero Indian Open in March and ended his rookie year 72nd on the Race to Dubai with seven top-10 finishes.

On 3 November 2019, at the WGC-HSBC Champions at the Sheshan International GC, Shanghai, China, he finished tied fourth, four strokes behind winner Rory McIlroy.

[4] Schwab's father Andreas represented Austria in the bobsleigh event at the 1976 Winter Olympics.