No.
Work experience is not must for admission in any management institute though in IIM's there is a weight-age for it but it is not mandate.

For your information CAT application process has already started and you can apply it from the link below:
CAT Application Form

Based on your performance in the exam, participating institutes will shortlist. In the second step of the selection process of CAT, shortlisted candidates have to appear for the second and final round, including GD or WAT and Personal Interview rounds.
The CAT 2017 selection procedure will be conducted separately at the participating institutes except for the new IIMs. CAT 2017 will be conducted by IIM Lucknow.

Hope this helps.
Good Luck!

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