India classes passport damage into two classes: damaged, and damaged beyond recognition (which means that your personal information page is damaged or unreadable).
Because this is only "damaged" you can get expedited service to have it replaced. The linked FAQ covers this situation:
In case your passport has not been damaged beyond recognition, i.e. passport number is legible, name is legible and photo is intact, then you can apply for re-issue of passport under the Tatkaal scheme. But, if passport has been damaged beyond recognition, then you cannot apply under the Tatkaal scheme. In that case, you need to visit Passport Officer at your nearest Passport Seva Kendra to get the passport on urgent basis.
The Tatkaal scheme can usually replace your passport within 1-3 working days.