The answer to it is No. There is no such requirement. Kindly note the following:
As far as Companies Act 2013 and Rules framed there under is concerned, both are silent with regard to the minimum and maximum face value or par value of each share.
However, currently SEBI requires companies who want to list on BSE to have minimum Re. 1 as minimum face value or par value of each share.
Therefore, it is possible that a private limited company can start its business with minimum face value of each share as Rs. 0.01 (i.e. 1 paisa),
Lets take an example: authorized share capital is Rs. 1 lac.
Thus a newly registered 1-paisa company would have 1 crore shareholder. In contrast to 1 lacs share holders possible with minimum face value of Rs. 1 each.
Kindly note earlier there was a requirement of minimum share capital of Rs. 1 lac which has been removed by amendment to Co Act 2013.
To conclude There is no minimum share face value for Indian Private limited company.