Despite receiving a compensation package this year worth £3.3m, the investors said Mr Hester's pay did not represent the "commercial rate" for the job he is doing.
Richard Buxton, head of UK equities at Schroders, which is the largest owner of RBS shares after the government and the bank's employees, with a 1.75pc stake, said Mr Hester's pay had become a "political football" as he gave evidence to a parliamentary committee yesterday.
"He can't at present be paid a commercial rate for doing that job," said Mr Buxton.
His comments were backed up by Robert Talbut, chief investment officer of Royal London Asset Management, which also owns shares in the bank.
"Its [RBS's] ability to retain a commercial management team is going to be severely inhibited if they [the bank's managers] do not believe they are going to receive a significant market rate," said Mr Talbut at the same hearing.
The support for Mr Hester comes after he last week said he thought the pressure on him over his pay was "unfair" and that he had been "within inches of quitting" after a row over his bonus earlier this year almost led to a vote in Parliament on his pay.
Mr Hester had been due to receive an all-share bonus worth £963,000, but waived the payment amid a public and political outcry.
Responding to the shareholders comments, former Liberal Democrat Treasury spokesman, Lord Oakeshott, said it was a case of "the tail trying to wag the dog".
"We own 82pc of it [RBS] and we didn't put the money in as a share price punt, we did it to get the bank lending again," he said.
Mr Hester's pay package is lower than that of the chief excutives of the RBS's two closest peers, Barclays and Lloyds Banking Group. As well as his £1.2m salary, the RBS chief received a £1.62m long-term incentive award, £420,000 towards his pension, and £26,000 of other benefits.
Lloyds boss, Antonio Horta-Osorio, received a package worth £4.56m even after waiving an annual bonus for 2011 that could have been worth as much as £2.39m, while Bob Diamond, chief executive of Barclays, was handed a total package worth £17.7m, though almost a third of this was in the form of a controversial £5.75m "tax equalisation" payment.
The scale of Mr Diamond's award led to a shareholder revolt at Barclays annual general meeting last month, with 32pc of investors failing to back the bank's remuneration report. Lloyds will hold its investor meeting on Thursday, but is not expected to face a similar level of discontent.
The investor support for Mr Hester came as bankers told MPs that the disposal of the state's holding in RBS would take at least five years and likely involve several offerings of the shares. Adam Young, co-head of equity advisory at Rothschild, said the government would probably have to begin selling its stake at a loss to drive interest in any disposal.
Discussing the potential sale of some of the holding to a sovereign wealth fund, Mr Buxton said he would be "disappointed" if the government pursued this option, adding that there was no "need to give the Exchequers money" to a large foreign investor.
