Glatz was born on 21 July 1943 in Vienna and grew up within the family firm, Glatz GmbH, an agricultural wholesale operation founded in 1892. His father Konrad Glatz managed the company from 1934 until his accidental death in 1971, at which point Fritz assumed leadership at age 28. The business dealt in grain, oilseeds, animal feed, and fertilizers, and was considered one of Austria's leading private agricultural wholesalers. Glatz's financial position as an industrialist allowed him to self-fund a motorsport career without professional sponsorship.
He is recorded as having begun racing in the mid-1960s in national Formula Vee events in Austria before taking a hiatus, returning to competitive single-seater racing in 1980.
Glatz entered the German Formula Three Championship in 1980 and continued in that series in 1981, also making appearances in the European Formula Three Championship. In 1981 he drove for the Walter Lechner Racing School, piloting a Ralt RT3 with a Toyota-Novamotor engine. His European Formula Two Championship debut came that same year, with a single start at Mantorp Park for Jo Gartner Racing in a Toleman TG280-BMW.
He began competing more regularly in Formula Two from 1982, entering ten races for Bertram Schäfer Racing in a Maurer MM82-BMW. He scored no points that season, his best result being an eighth place. In 1983, racing for Emco Sports in a Spirit 201-BMW, he again started ten races but managed only two finishes, remaining pointless. The 1984 season finally brought championship points: still with Emco Sports but switching mid-season to a March 842 prepared by Mader engines, he took a sixth place at Donington Park — his career-best Formula Two result — worth one point and 15th in the final standings.
When International Formula 3000 replaced Formula Two in 1985, Glatz made two attempts with Équipe Oreca in a March 85B-Cosworth, including a DNS at Silverstone; he did not finish either start. In 1986 he drove nearly a full season for Eddie Jordan Racing in a March 86B-Cosworth but managed only a best result of 14th place, with one failure to qualify at Pau. He also made two starts in the World Sports-Prototype Championship that year, for Roy Baker Racing at Jerez and Martin Schanche Racing at the Nürburgring, without scoring in either.
After a year away from racing in 1987, Glatz returned to Formula 3000 in 1988 at the age of 45 with Racetech 3000 in a Reynard 88D-Cosworth. Three failures to qualify in six attempts prompted a mid-season switch to Madgwick International in a Lola T88/50; his best finish across the campaign was 12th. He made three additional World Sports-Prototype Championship starts in 1988. In 1989 he made a single appearance in the inaugural British Formula 3000 Championship.
During the 1990s Glatz competed in the Interserie series in Germany under the name Frederico Careca, and also made scattered sports car starts in various European events.
On 14 July 2002, Glatz was competing in a EuroBOSS event at Autodrom Most in the Czech Republic, driving a 1996-vintage Arrows Footwork FA17 Formula One car. His car bounced over a kerb, became airborne, and somersaulted. Glatz died from the injuries he sustained. He was 58 years old and died one week before what would have been his 59th birthday.