I'm not sure about whether kings and royals count as politicians for the scope of the question, but several royals took part in the Olympics and some of them got a medal.
The outstanding examples are:
King Olaf V of Norway, who won a gold medal sailing in the 1928 Olympic Games, when he was still the heir to the throne.
King Constantine II of Greece, also ...
According to Wikipedia, the ancient Olympic Games count among their winners:
Philip II of Macedon (father of Alexander the Great, on the latter's birthday no less)
(However, English Wikipedia doesn't give any details on which event or even which year they won, it just lists them in their "Ancient Olympic Games" box under "...
Ukrainian Zhan Beleniuk has been a parliamentary deputy (equivalent to MP) since 2019, and has competed at the Olympics in Greco-Roman wrestling, winning silver in 2016 and gold in 2020. (Borderline on the timing criteria, since it was only in 2020 that he was both a medallist and politician simultaneously, although he had been both individually before 2020....
William Grenfell competed in the 1906 Intercalated Games in team épée. He was a UK MP until December 1905 until raised to the peerage and was - if I understand how the House of Lords worked in the early 20th century - therefore a member of the House of Lords at the time.
Various members of the British Royal Family have won high level showjumping medals:
Princess Anne, the daughter of Queen Elizabeth II, won various titles including the 1971 European Eventing Championship.
Mark Phillips, Anne's (now ex-)husband, won an Olympic gold medal in 1972 (before he was married to Anne) and a silver in 1988. Phillips also won a number ...