She was born Judith Therese Evans in Detroit, Michigan. Her mother, Mollie Ann (née Greer), is a hospital administrator, and her Father, Rich Evans, is a mechanical Engineer. Her mother was once a nun who left the convent after eight years, when she was "kicked out" for wild behavior, including owning a red bathing suit. Greer was raised Catholic and grew up in Redford Township and Livonia. She attended Churchill High School and graduated from The Theatre School at DePaul University in 1997. She later adopted her mother's maiden name for her stage name, as there were several other actresses named Judy or Judi Evans.
Greer had small parts in the films What Women Want (2000) and The Wedding Planner (2001). She was cast in a 2002 pilot for NBC alongside Stephen Colbert, Untitled Ken Finkleman Project (Imagine Entertainment), based on the Canadian show The Newsroom from Ken Finkleman. Colbert portrayed Finkleman and Greer played his sister.
Greer had recurring role on the Fox comedy series Arrested Development (2003–2005, 2013), playing Kitty Sanchez in 10 episodes total and appearing in each of the series' three original seasons. In an August 2009 interview, Greer said that she is most recognized for this role. She had supporting roles in Jawbreaker (1999), What Women Want (2000), The Wedding Planner (2001), Adaptation (2002), 13 Going on 30 (2004), The Village (2004), Elizabethtown (2005), 27 Dresses (2008), and Love Happens (2009). Greer has made guest appearances on Just Shoot Me! (2003), CSI: Miami (2005), My Name Is Earl (2006), It's Always Sunny in Philadelphia (2007, 2011), Californication (2007–2008, 2012), ER (2009), House (2009), Modern Family (2010), The Big Bang Theory (2010), How I Met Your Mother (2010) and Warren the Ape (2010). She took on a starring role in the ABC sitcom Miss Guided (2008), but it was canceled in its first season. She also starred in the indie satire Visioneers (2008).
In April 2008, Greer appeared as a yoga instructor in the "Get a Mac" ad series featuring John Hodgman and Justin Long. Greer starred in a CBS sitcom entitled Mad Love, which premiered in February 2011 as a mid-season replacement. The show was canceled after the first season.
In November 2011, Greer was honored with the Independent Spirit John Cassavetes Award at the Denver Film Festival, where two films featuring Greer were in the festival's programming, including a red carpet screening of Alexander Payne's The Descendants and the Jay and Mark Duplass' Jeff, Who Lives at Home. She is the first Actress to be honored with the award. She played the gym Teacher Miss Desjardin in the 2013 film adaptation, Carrie, alongside Chloë Grace Moretz and Julianne Moore, and played female chimp Cornelia in Dawn of the Planet of the Apes (2014). In 2014, Greer made her directorial debut, with a short film for AOL, Quiet Time. Greer starred with Nat Faxon in the FX comedy series Married, which premiered in July 2014.
Greer grew up Catholic, although at age 10 she convinced her parents let her go to a Presbyterian church as she thought she would be closer to God there, although the real reason was she thought there were cuter boys at that church. During a 2014 interview, Greer stated that she is no longer a practicing Catholic. In 2014, she told Glamour, "I had been wanting to try and learn how to meditate, and I did research on the different types of meditation. TM seemed the easiest, and I liked that it wasn't religious in any way."
In 2015, Greer co-starred in the films Tomorrowland, Jurassic World and Ant-Man, among others. In 2016, she debuted in the lead voice role of Beep in the Netflix children's animated programs, Ask the StoryBots and StoryBots Super Songs. In 2017, she reprised her role as Cornelia in the film sequel War for the Planet of the Apes. In 2018, she will reprise her role as Maggie Lang in the superhero film Ant-Man and the Wasp and she will play the daughter of Laurie Strode in the next installment of the Halloween franchise.