Panjabi was born in Edgware, London, to Govind and Padma Panjabi, both Sindhi Hindu emigrants from India. Her ancestry belongs to Sindh, now in Pakistan; after partition, her parents settled in India. She graduated from Brunel University with a degree in management studies in 1996. She is also classically trained in ballet.

Panjabi married Rajesh Nihalani, a bespoke tailor, in 1998. Archie had to leave him at home in England for her first nine months of their marriage. She moved to New York to work on the show The Good Wife.

Panjabi has appeared in film and television; from early appearances in the 1999 comedy film East is East to the BBC television series Life on Mars. Her first Hollywood role, as a British diplomat, was in the Oscar-winning The Constant Gardener, released in 2005. One of her highest profile film roles was in the 2002 comedy release Bend It Like Beckham. Panjabi then landed the role of witty and wisecracking office colleague Gemmain in the 2006 Ridley Scott directed romantic comedy A Good Year, alongside Russell Crowe and Marion Cotillard.

Panjabi was awarded Chopard Trophy in Cannes Film Festival in 2007. She was nominated for three Primetime Emmy Awards for Best Supporting Actress in a Drama Series for The Good Wife, winning in 2010. She won an NAACP Image Award in 2011 for Outstanding Supporting Actress in a Drama Series for the same role. She was also nominated for three SAG Awards with her co-stars of The Good Wife for Outstanding Performance by an Ensemble in a Drama Series.

She provided the voices for several characters in the British children's television animation Postman Pat. She lent her voice to the video game Dead Space: Extraction. Panjabi appeared on the BBC Four World Cinema Award show in February 2008, arguing the merits of five international hits such as The Lives of Others and Pan's Labyrinth with Jonathan Ross and Christopher Eccleston. In 2009 she portrayed an MI5 agent in the French movie Espion(s), and in the same year she joined the cast of the new CBS television series The Good Wife as Kalinda Sharma.

Panjabi was appointed the first Pratham USA Ambassador representing the largest educational movement in India. She is a Celebrity participant in the Rotary International's "This Close" public Service campaign to end polio. In support of women's rights, she has partnered with Amnesty International to head their Stop Violence Against Women campaign to change the "no recourse to public funds" rule that traps women in a cycle of violence. On 9 February 2011, Panjabi walked in The Heart Truth's Red Dress Collection Fashion Show to increase awareness of the danger of heart disease, the number one killer of women. The Harvard Foundation and Office for the Arts at Harvard University invited Panjabi to participate in their Artist in Residence Program in Cambridge, Massachusetts, to share her creative process as an Actress.

In 2010, she played Saamiya Nasir in the British comedy The Infidel. On 28 May 2012, she was cast as Tanya Reed Smith, a pathologist, in BBC Two drama series The Fall. Panjabi appeared as Blaise in the BBC World Service radio series Westway. After leaving The Good Wife in 2015, she guest starred in Fox comedy series Brooklyn Nine-Nine. She joined the cast of Shetland series 3 to return in series 4 in February 2018.

In 2016, it was announced that she will star in ABC anthology drama series The Jury as the show's protagonist, Kim Dempsey. She also joined the cast of NBC drama Blindspot.