He was born in Prague, Czechoslovakia, into a family of some wealth and notability. His undergraduate education began in 1938 when he enrolled to study natural sciences at Charles University. His studies were interrupted the following year when universities were shuttered under the German occupation. Working under the supervision of  at Bulovka Hospital, and in a rudimentary laboratory in the basement of his parental home, he discovered a polarographic method of measuring fast chemical reactions. He was awarded a doctorate for this research when Charles University reopened in 1945.
In 1943, he joined a research group at the Fragner pharmaceutical company near Prague that was working to develop a penicillin variant. Despite working in secrecy and isolation under onerous wartime restrictions, the group managed to first separate and then test an antimicrobial drug. Wiesners role included ensuring an adequate supply of the antibiotic by extracting and purifying the substance from the test subjects urine following treatment.
From 1946 until 1948 he conducted postgraduate research in organic chemistry under Vladimir Prelog at ETH, Zürich, funded by a Rockefeller fellowship. Wiesner immigrated to Canada in 1948 to take up a position at the University of New Brunswick, Fredericton. Apart from a two-year spell with the pharmaceutical company Ayerst in Montreal, he remained at UNB for the remainder of his career. In 1981, Wiesner became a founding member of the World Cultural Council. He died of lymphoma in 1986.