Fox, which now owns 39.1% of Sky, is trying to buy full control of the business in a deal that would value it at £18.5bn.
More than 28% of shareholders voted against Mr Murdoch's comeback as chairman last year, four years after he stood down from the position in the wake of the phone-hacking scandal at the News of the World.
Later on Thursday, shareholders voted in favour of the re-election of Murdoch´s son James as chairman.
Meanwhile, the takeover of Sky is being held up by a United Kingdom investigation into the proposed deal worth Â£11.7 billion.
"The board notes the significant vote against resolution 3, the director's remuneration report and resolution 12, the re-election of James Murdoch, and will continue to engage with shareholders to understand their views as part of its ongoing programme of engagement".
The shareholder, Hugh Lawson, said: "I think the board lacks independence".
Today's update comes as Sky awaits a decision from the competition watchdog on a proposed takeover by 21st Century Fox. "Fox is getting a sweetheart deal out of this and mainly I think it's because of the lack of independence on the board".
21st Century Fox (21CF) has welcomed the publication by the CMA of the Issues Statement.
Its bid, which is strongly opposed by some lawmakers and is subject to lengthy regulatory scrutiny, hangs over the European pay-TV group, which reported quarterly results earlier on Thursday.
Like-for-like revenues were up five per cent to £3.3bn in the three months to 30 September, from £3.1bn this time past year.
"We continue to see strong customer demand for our products and services, so net customer additions in the quarter are 50 percent higher than a year ago", Darroch told reporters.
He pointed out that in addition to Sky's existing markets - the UK, Ireland, Germany, Austria and Italy - the company had just launched consumer streaming services in Spain and Switzerland.
"We've had a strong start to our new financial year with good revenue growth and excellent profit growth as investments we've made come through", the group's chief executive Jeremy Darroch commented in the statement, adding that fantasy drama Game of Thrones had "become the most watched series ever on Sky", while the group's home-grown drama Riviera had achieved 20 million downloads.
Shares in 21st Century Fox were flat at $25.50 in light-volume trading.