Krause was born in Alexandria, Minnesota, to a mother who taught second grade and a father who was a high school English teacher. He was raised in Roseville, Minnesota, a suburb of St. Paul. He has two siblings, Michael and Amy. Krause graduated in 1987 from Gustavus Adolphus College in St. Peter, Minnesota, with a degree in English literature. He also has a Master of Fine Arts degree in Acting from New York University's Graduate Acting Program at the Tisch School of the Arts.
In the early 1990s, Krause made a number of guest appearances on television shows such as Seinfeld, Beverly Hills, 90210 and Ellen. He was a cast member of Carol Burnett's sketch comedy series Carol & Company from 1990-1991. Starting in 1996, Krause appeared in a recurring role as Cybill Shepherd's son-in-law Kevin on her sitcom Cybill for four seasons. From 1998 to 2000, Krause also portrayed the character Casey McCall on the ABC network's comedy Sports Night. Although the show received considerable critical acclaim, it struggled to find an audience and was canceled after two seasons. Krause starred in the HBO drama series Six Feet Under from 2001 to 2005. He received seven award nominations (including three Emmy nominations) for his portrayal of funeral director Nate Fisher.
Krause appeared on Broadway in the summer of 2004 in a revival of Arthur Miller's After the Fall. In December 2006, he played the lead role, Detective Joe Miller, in the Sci Fi Channel miniseries The Lost Room. From 2007 to 2009, Krause portrayed young lawyer Nick George in ABC's drama Dirty Sexy Money alongside veteran actor Donald Sutherland. He had initially turned down the role three times. He also served as a series producer. From 2010–2015, he played Adam Braverman in the NBC comedy-drama Parenthood. He directed three episodes for the show. Krause appeared in the 2011 fantasy film Beastly, based on Alex Flinn's 2007 novel of the same name. From 2016–2017, he starred opposite Mireille Enos in the ABC crime drama series The Catch, produced by Shonda Rhimes. In August 2017, Krause was cast in the Ryan Murphy-produced drama 9-1-1, which focuses on the lives of first responders. 
- His character, Bobby once worked in the Minnesota Fire Department before the start of the series, in the same state where he was born.