As a student at Espergærde Ungdomsskole Bodnia joined the theatre group, performing mainly in comic roles. When he was 16 his mother suggested he apply for a place at National Theatre School in Copenhagen. His first application failed, but he gained entry on his second attempt a year later in 1987.

In his film debut En Afgrund af frihed (An Abyss of Freedom) (1989) he played a small supporting role as a bouncer. One of his first roles after graduation in 1991 was as Patrick Bateman in a stage version of American Psycho, and he was subsequently often typecast as violent, brutal characters. Bodnia's first leading role in a film was in Bulldozer (1993), directed by Maria Sødahl. His breakout role came a year later in Ole Bornedal's horror film Nightwatch (1994).

Despite this success it was two years before his next film, Nicolas Winding Refn's Pusher (1996), and then Winding Refn's Bleeder (1999). He has since appeared in Terribly Happy (2008), and in three Lasse Spang Olsen films: In China They Eat Dogs (1999) and its sequel Old Men in New Cars (2002), and in Den Gode Strømer (2004), which he co-wrote with the Director. Bodnia has also appeared in several Norwegian films, including Himmelfall (2002), Monstertorsdag (2004), and Tomme Tønner (2010). He appeared in the 2011 Indian English comedy film Delhi Belly playing a Russian smuggler. In 2014 he appeared as the eponymous Iranian interrogator Rosewater, directed by Jon Stewart. As to his role, he said: "It was a tough job because I'm Jewish. I'm playing a guy who really hates me and wants to destroy my country."

In 2001 Bodnia co-wrote and directed the short film Escape - Flugten fra ensomheden ("Escape - FLIGHT from loneliness"). In early 2014 he directed readings of The Tailor's Tale, a play based on his Jewish grandfather's experience of life in Copenhagen under Nazi occupation, written by his cousin Alexander Bodin Saphir, and performed at the Scandinavia House–The Nordic Center in America in New York.

Bodnia has appeared regularly on television, making his first appearance in the historical mini-series Snapphanar in 2006. He appeared in three episodes of the first season of the crime series The Killing (2007) (Danish: Forbrydelsen), and in two episodes of the comedy drama Hvor fanden er Herning? ("Where the hell is Herning?") (2009), before returning to crime series, appearing in episodes of the Swedish Kommissarie Winter (2010), Den som dræber ("Those Who Kill") (2011), and the German/Swedish Der Kommissar und das Meer ("The Inspector and the Sea") (2012).

In 2009 he won the 62nd Bodil Award for Best Actor in a Supporting Role. In 2014 he won the Monte-Carlo Television Festival Award for Outstanding Actor in a Drama Series.

Bodnia played the Danish detective Martin Rohde in the first two series of the Nordic noir crime television programme The Bridge (Broen|Bron) (2011–present). Created and written by Hans Rosenfeldt, it is a joint creative and financed production between Sweden's Sveriges Television and Denmark's DR. It has been shown in over 100 countries. Although Bodnia signed for the third series, he dropped out, reportedly unhappy with the development of his character. He also voiced concerns in an interview about working in Malmö, due to the city's problems with anti-semitism, which had made his decision to leave the series easier. He said: "it’s not very nice and comfortable to be there as a Jewish person."

Bodnia was born in Copenhagen and grew up in Espergærde. He came from a Jewish family – originally from Poland and Russia. When asked in 2011 whether religion had been an important aspect of his life, he said, "No, but I believe in nature". In 2014 he said: "I'm half-Russian, half-Polish and all Jewish."