Good question Priyanka. In my experience over last 16 years, I've found following 3 skills to be critical for success in digital marketing:
Communication Skills (especially written): Most of the profiles in digital marketing (across SEO, SEM, Social Media Marketing, Email Marketing) require good communication skills.
Analytical Skills: Given there are no fixed solutions or formulas to be successful in digital marketing, ability to assess a situation and accordingly come up with an appropriate solution is another key skill for someone to grow in digital marketing industry. It's one of the reasons why engineers with strong analytical skills are doing well in digital marketing industry.
Passion for Digital Media: Given the dynamic nature of this industry, one has to remain a student of this industry to stay ahead. If someone is genuinely passionate about digital media and open to embrace changes, success is going to be natural.
Hope this helps. I would love to hear other's views and experiences as well. Interestingly, I am planning to write an article about this area for Economic Times.