Yes. There are more than one law against verbal abuse in India.
Section 294 of the Indian Penal Code punishes anyone who does any obscene act in public, says any obscene or abusive word in public, or sings or recites any obscene song near a public place. The punishment is either imprisonment for a description of term (generally 2 years), or fine, or both.
(Courtesy: Office on Women's Health)
Section 66 An of the IT act punishes anyone who sends anything through any communication device any offensive text or information. Sending any text which may insult anyone in any way also falls under this section.
For women in India, there is section 509 of IPC. According to this section, anyone who makes an offensive comment or gesture to violate the modesty of a woman shall be punished. Making any kind of sound, exhibiting any object, or intruding the privacy of any woman in any way shall also be punished with imprisonment under this act.