NMC shares were up 5% to 738.8p by Monday afternoon.
"Today's freakish disclosures about even more pledges and debt validate that the cockroach theory is alive and well - what we found is likely just the tip of the iceberg", Muddy Waters' Carson Block said in a statement.
Shetty was not immediately available for comment on the NMC statement, which said the company was investigating. "As for the notion that NMC might receive private equity bids, it's hard for us to believe they would survive due diligence".
'This suggests that the holdings and interests of Dr. B.R. Shetty, H.E. Mr Saeed Mohamed Butti Mohamed Khalfan Al Qebaisi and Mr Khaleefa Butti Omair Yousif Ahmed Al Muhairi have been incorrectly reported historically to the Company and the market, ' the statement said.
Former FBI boss Louis Freeh is leading a separate independent review committee appointed by London-listed NMC to investigate the Muddy Waters allegations. The news about founder Shetty's stake increased speculation that NMC's biggest shareholders faced margin calls and have been forced to sell shares.
NMC Health disclosed preliminary buyout approaches from private equity firms KKR and GK Investment on Monday, lifting its shares, which have dropped dramatically since Muddy Waters a year ago queried its financial statements.
KKR, which bought pharmacy chain Boots for £11.1bn in 2007, said: "KKR confirms that it has not made a proposal nor discussed with NMC the terms of any possible offer, and that it does not intend to make an offer for NMC".
GKSD is being consulted by GK Investment, which approached NMC on its behalf, the agency stated. The company has said the allegations are false and misleading. NMC's $107m redevelopment of NMC Royal Women's Hospital in Abu Dhabi "contains numerous red flags", the short seller said. NMC also appears to have paid too much for a stake in Premier Care Home Medical and Health Care LLC, the report alleged.
NMC's margins are "too good to be true" relative to peers, Muddy Waters, which is shorting the company's stock, also said.
A native of India, Shetty moved to Abu Dhabi in 1973 and founded NMC in the 1970s.
-With assistance from Filipe Pacheco, Lisa Pham and Jan-Henrik Förster.