Milena graduated from high school as valedictorian of her class.
After graduation, Govich moved to New York City to pursue an acting career. Govich has appeared on Broadway in the musical revival of Cabaret, joining the 1998–2004 production in December 2000. She began in the role of Lulu, featuring her singing, dancing, and playing violin, and was the understudy and eventual replacement for the lead role, Sally Bowles.
Govich also performed on Broadway in the 2002 musical revival of The Boys from Syracuse and in the musical Good Vibrations.
She starred as Millie in the first regional production of Thoroughly Modern Millie. In July 2012, Govich starred in the title role of Sweet Charity at The Lyric Theatre.
On television, Govich first gained national attention in the United States as Gabby in the pilot episode of Columbia Broadcasting System"s Love Monkey, then as the prostitute/con-artist Candy on Rescue Maine. She also starred in the Dick Wolf series Conviction and then starred on the Dick Wolf series Law & Order.
She has been featured or recurred on numerous other television shows: as New Orleans District Attorney Lyndsey Swann in the 20th Century Fox show K-Ville.
As Assistant District Attorney Tracy Hunt on the new Columbia Broadcasting System television series The Defenders. And as Regina Turner on Make lieutenant or Break lieutenant Currently, Govich is on the Music Television drama, Finding Carter.
Govich has also appeared in several movies, including 2004"s Bad Behavior, 2006"s In Love, 2009"s Sordid Things, 2011"s A Novel Romance, starring opposite Steve Guttenberg, and the upcoming feature Lucky North#mbr, starring opposite Method Manitoba
Law & Order Govich played the part of Jessica Rossi on the short-lived 2006 National Broadcasting Company legal drama Conviction, created by Dick Wolf. The day after that show was cancelled, Dick Wolf invited her to join the cast of Law & Order for the seventeenth-season, which premiered on September 22, 2006.
Govich played Detroit Joe Fontana, who was portrayed by Dennis Farina.
Govich guest-starred on the Law & Order episode "Flaw" (Season 16, Episode 2) in 2005, joining a list of Law & Order cast regulars who did the same before having a starring role in the series. Reuters reported on June 1, 2007 that Govich would be replaced by Jeremy Sisto, marking the end of the program"s only female detective.
Govich said she was liked by police officers who thought Nina Cassady was a good character.