Finally, I got the answer for the long pending question in my mind. Thanks to Quora.
How do you say “I am missing you” in Tamil?
Though we can’t expect a literal translation in Tamil, I felt this to be close enough to convey the meaning.
நான் உன் இன்மையை உணர்கிறேன் (Naan un inmaiyai unargiren).
i.e., I’m feeling your absence.