According to insiders, the pair couldn't devote enough time to each other as the 24-year-old beauty films her hit teen drama in Atlanta, while Derek shoots the dancing contest in Los Angeles.
A source told Us Weekly magazine: "The distance was too much to handle."
The fledgling couple, who began seeing each other in early September, reportedly felt their romance had "played itself out," according to another source.
Nina is good friends with Derek's sister Julianne Hough, 25, and met the 28-year-old professional dancer through her.
The Safe Haven actress is thought to "understand" the reason for the split and has no "hard feelings" towards her pal Nina.
Derek was reportedly "smitten" with his new girlfriend when they first emerged as a couple and exclaimed to friends "he hasn't felt this way for a girl in a long time."
The brunette beauty began seeing Derek just four months after ending her three-year relationship with Vampire Diaries co-star Ian Somerhalder.
Derek was previously linked to British singer Cheryl Cole after appearing in the music video for her song "Parachute."