Veena began her acting career in the late 1990s, initially appearing in teledramas (Sri Lankan television dramas). Her breakthrough performance came in 1998 with the teledrama "Kavitha", which earned her widespread recognition. Throughout her career, she has starred in numerous critically acclaimed and commercially successful films, including "Siri Parakumene" (2001), "Aha O/L" (2001), and "Loku Duwa" (2003).