Moser began racing in the early 1960s with Alfa Romeos, gaining experience in club events before moving to single-seater formulae in 1964. He built his reputation in European Formula Three and the South American Temporada series and competed in Formula Two before targeting Formula One.
Moser's first attempt at a Grand Prix came at the 1966 German Grand Prix at the Nürburgring Nordschleife, where he entered a Formula Two Brabham BT16 in his own name for a race that permitted F2 machinery alongside the new F1 cars. The engine failed in practice and he did not start.
His official World Championship debut came on 15 July 1967 at the British Grand Prix at Silverstone, driving a Cooper T77-ATS entered by the Swiss Charles Vögele team. He returned with the Vögele organisation in 1968 in a Brabham BT20 fitted with a Repco V8. At the 1968 Dutch Grand Prix he finished fifth to score two championship points; later that season he added a sixth place at the United States Grand Prix for one further point.
For 1969 Moser established his own team, the Silvio Moser Racing Team SA, headquartered in Lugano and backed by Aldo Sonvico and Aldo Pessina. The team purchased a Brabham BT24-Cosworth and entered several championship rounds. He retired at Monaco (driveshaft) and at the Dutch Grand Prix (ignition), finished seventh in France, and placed sixth at the United States Grand Prix to collect his final championship point.
In 1970 Moser commissioned a new car from designer Guglielmo Bellasi rather than continue with a customer chassis. The resulting Bellasi F1 70, painted red, was described by chief mechanic Beat Schenker as "full of ideas" but not what the team needed in practice. Of five qualifying attempts that season the team achieved a single start, at the 1970 Austrian Grand Prix, where Moser retired after 13 laps with a radiator failure. He made one further championship start at the 1971 Italian Grand Prix, driving the Bellasi for the Jolly Club of Switzerland before retiring. The car was subsequently sold to Tom Wheatcroft and exhibited at the Donington Grand Prix Collection.
Across twenty entered World Championship events, Moser achieved twelve starts and scored three points in total.
Moser was a consistent Formula Two competitor across several seasons. In 1968 he drove a Tecno TF68 for the Charles Vögele Racing Team. After the Bellasi programme concluded he returned to Formula Two with Brabham machinery in 1971 and 1972, then raced a Surtees TS10 in 1973. He achieved a second-place finish at the Monza Lottery Grand Prix, one of his stronger results in the formula. His Formula Two entries were made under various organisers including the Jolly Club of Switzerland and Scuderia del Lario.
On 25 April 1974, Moser was competing in the 1,000 km sports car race at Monza, driving a Lola T294-BMW. He was involved in a serious accident during the race. He never regained consciousness and died thirty-one days later on 26 May 1974 in Locarno, Switzerland.