In case of Private Limited Companies;
Section 29 (1) (b) of Companies Act 2013 includes Private Limited Companies also w.e.f. 14.08.2019. However, the class of companies to which it should apply is yet to be prescribed (last checked on 4th July 2020).
Presently the Company law makes it mandatory only for Unlisted PUBLIC Limited companies to get their shares dematerialized as soon as possible. And, if somebody subscribes or transfers any shares of an unlisted Public companies on or after 02.10.2018, then he can do so only after getting the shares dematerialized.
Therefore, as of now, no law necessitates Dematerialization of shares of Private Limited companies in case of transfer.