Kozlowski was born and raised in Fairfield, Connecticut, the daughter of Helen E. (Parniawska) and Stanley M. Kozlowski. She is of Polish descent. She is a 1976 graduate of Fairfield's Andrew Warde High School. Kozlowski graduated from the Juilliard School's drama division in 1981.

Kozlowski debuted in the 1981–1982 off-Broadway production How It All Began. She played "Miss Forsythe" on Broadway in Death of a Salesman and in 1984 took the same role in the film version of 1985.

Her big break came in 1986 when she was cast as the female lead, opposite Paul Hogan, in the Australian film Crocodile Dundee, in which their on-screen chemistry spilled over into a real relationship. Two years later, she revisited her starring role with Hogan in Crocodile Dundee II. Also in 1988 she starred with Bill Paxton, Tim Curry and Annie Potts in Pass the Ammo and the TV miniseries Favorite Son.

Kozlowski married Hogan on May 5, 1990, after he divorced his wife Noelene, to whom he had been married twice over the previous 32 years, from 1958 to 1981 and 1982 to 1990. Kozlowski and Hogan have one child, a boy named Chance. Kozlowski had been married once prior to her marriage to Hogan. In October 2013, Kozlowski filed for divorce from Hogan, citing irreconcilable differences.