Matthias Jacob won the bronze medal at the 1984 Winter Olympics at Sarajevo over 10 km, placing ninth four years later over 20 km. In the relay he placed fourth at Sarajevo and fifth at Calgary. In 1981, 1982 and 1987 he was World Champion in the relay, placing second in 1983, 1985 and 1986. Jacob also won a silver medal over 10 km in 1987. Domestically he claimed three titles over 10 km (1981, 1982, 1986), and one title over 20 km in 1986, while in 1983 he was runner-up and he placed third in 1982. He won East German titles in 1981, 1982 and 1987 with the ASK Vorwärts Oberhof relay team, and was runner-up 1983, 1984, and 1986, placing third in 1985 and 1988.
Jacob later married cross country runner Carola Anding and ran a practice for sports physiotherapy with her in Floh-Seligenthal. They regularly worked for the German national team. During his sport career he was employed by the Nationale Volksarmee (NVA). After German reunification it became known that Jacob had worked for the State Security Service (Stasi) as an IM (internal employee).