Zaremba was born in Poznań, Poland. He came to Sweden in 1969 where he worked as a construction worker during the 1970s. In his youth, he was active in the League Communist (Swedish: Förbundet Kommunist), but abandoned his communist views when the group was dissolved in 1982. He earned a B.A. in the history of ideas from Stockholm University in 1988. He started writing for the newspaper Dagens Nyheter in 1989 and in 1994 he was recruited to the editorial team of the now defunct magazine Moderna tider.
In 1997, Zaremba became famous after he wrote a series of articles in Dagens Nyheter about the compulsory sterilization program active in Sweden from the mid-1930s until the mid-1970s. The article sparked much debate in Sweden and led to a government inquiry into the matter.
In 2005 he wrote a series of articles about a labor dispute involving foreign construction workers in Vaxholm. For these articles he was awarded the Stora Journalistpriset ("Great Journalist Award") and Hasse Olssons pris till årets ekonomijournalist ("Hasse Olsson's Award for Business Journalist of the Year") in 2006. In 2005 he also received Gösta Bohman-stipendiet ("Gösta Bohman Award) and a prize from the Swedish Academy through its own funds.
Zaremba has been married since 1982 to the author Agneta Pleijel.
- Zaremba, Maciej; Pieniowski, Håkan (1983). Rzeszów : bland polska bönder (in Swedish). Stockholm: Öppna ögon. ISBN 91-85906-15-8.
- Zaremba, Maciej; Bischofberger, Erwin (1985). Arbete före kapital : den katolska kyrkans sociallära (in Swedish). Stockholm: Brevskolan på uppdrag av Svenska kristna socialdemokratiska förbund. ISBN 91-574-1199-9.
- Zaremba, Maciej (1992). Minken i folkhemmet : [essäer] (in Swedish). Stockholm: Timbro. ISBN 91-7566-250-7.
- Zaremba, Maciej (1999). De rena och de andra : om tvångssteriliseringar, rashygien och arvsynd (in Swedish). Stockholm: Dagens Nyheter. ISBN 91-7588-328-7.
- Zaremba, Maciej (2000). Kyrkan & friheten : en debattbok om den fria Svenska kyrkans identitet och demokrati (in Swedish). Gothenburg: Cordia. ISBN 91-86082-88-4.
- Zaremba, Maciej (2006). Den polske rörmokaren och andra berättelser från Sverige (in Swedish). Stockholm: Norstedt. ISBN 91-1-301606-7.