The award "locks in unprecedented high pay opportunities for the next decade, and seemingly limits the board's ability to meaningfully adjust future pay levels in the event of unforeseen events or changes in either performance or strategic focus," ISS said on Thursday.
The advisory firm also flagged that a big part of the award could be earned even if Tesla, which reported its worst ever loss in the fourth quarter, does not sustainably make profits in the future.
"Musk's financial interests are already strongly aligned with Tesla; it is questionable whether an additional $2.6 billion grant is necessary or appropriate to further align his interests when he already owns a 22 per cent stake in the company," ISS added.
Some analysts have questioned whether billionaire Musk's other interests, from space exploration to tunnel boring technology, are a distraction at what is seen as a critical time for Tesla.
Musk took to Twitter on Thursday to call on U.S. President Donald Trump to challenge Chinese auto trade rules.
Tesla shares were down half a per cent at $327.25 after markets closed on Thursday.