Kohan was born to a Jewish family in Los Angeles, California, the daughter of Rhea Kohan (née Arnold), and Alan W. "Buz" Kohan. She is the youngest of three siblings, the other two being twins Jono and David. Much of the family is in show business:
Kohan's paternal grandparents were Charles Kohan and May E. Charles. He was born in Romania in 1902, while she was born in New York City, to parents from Russia. The two knew each other from childhood, growing up in a New York City settlement house on the Lower East Side of Manhattan.
Kohan says that her father was the "king of variety television in his day," writing and producing the Oscars and other variety shows. Her mother was a novelist. She grew up in Beverly Hills, California and attended Beverly Hills High School, graduating in 1987. She first attended Brandeis University, and transferred to Columbia University as a sophomore, where she graduated, with a degree in English language and literature, in 1991.
Kohan's first job in the industry was with Fresh Prince of Bel-Air, of which Kohan wrote one episode, and later said was a "rough entrance" to the business. After a series of writing jobs on shows such as Mad About You, Tracey Takes On..., and Friends, she collaborated with her brother, David Kohan, writing an outside script for Will & Grace. The siblings also worked together on the sitcom The Stones for CBS, which was ultimately unsuccessful. She has discussed the differences between her and her brother's career saying, "David took the big, commercial, funny route; I was always a little darker personally, and not terrific within the system. I had to make my own way."
Kohan was the creator of the Showtime dark comedy-drama television series Weeds, which she executive produced as showrunner and head writer at her writing studio, Tilted Productions, in Los Angeles, California throughout its entire eight season airing.