BCCI president Ganguly and secretary Shah will chair the meet and will discuss adding two new teams to the IPL from 2022.
The post of vice-president fell vacant after Mahim Verma quit the post and returned to his home state, Uttarakhand where he was elected as secretary of the state's association once again.
Shukla had earlier been a vice-president during N Srinivasan's regime and was also a popular chairman of the IPL governing council.
Former IPL chairman Rajiv Shukla said it may be impossible for the tournament to take place.
45 days after Verma officially resigns, the BCCI will hold elections for the post of vice president.
The committee will be led by a commissioner, who will investigate the corruption issue and submit reports in 15 days.
Arjun has previously been a part of the Mumbai Under-14, Under-16, and Under-19 teams.
Umpires are even instructed to use technology if needed to avoid errors.
IPL chairman Rajiv Shukla confirmed that Decision Review System (DRS) will be utilised if a team challenges an umpiring decision in IPL 2018.
The current situation in Pakistan is not conducive for India to resume cricketing ties with it and there is no chance of the two countries playing a match in the near future.