The Local Authority Pension Fund Forum (LAPFF), whose 54 members have combined assets of around £100bn and own around 1% of Sky, wants the board of Sky to "put distance" between the pay-TV giant and the phone hacking controversy by making changes to its corporate governance.
LAPFF said that it has undertaken "extensive research" and also engaged with Sky directly, leading to the belief that the firm would "benefit from the appointment of an independent chair".
The forum has issued a voting alert to its members ahead of Sky's annual general meeting on November 29.
The fund's action has particularly been motivated by James Murdoch's second appearance in front of the House of Commons culture, media and sport select committee yesterday to answer more questions about phone hacking.
LAPFF said that due to concerns over Murdoch's "independence" and the "ongoing risk of reputational contagion from his association with the phone hacking scandal", it is urging members to oppose the News Corporation executive's re-election as Sky chair.
However, LAPFF has recommended the re-election of Sky's lead non-executive director Nicholas Ferguson "in recognition of the company's willingness to engage with the forum".
LAPFF chair Ian Greenwood said: "BSkyB shareholders need to see some distance put between the company and the scandal engulfing News Corp, but this is not possible without governance reform.
"While the Forum acknowledges James Murdoch's contribution to BSkyB's past success, we believe that the company would now benefit from having a new independent chair."
The phone hacking scandal has resulted in the closure of News Corp's News of the World and the withdrawal of Rupert Murdoch's bid to acquire the 60.9% of Sky that he does not already own.
James Murdoch was given the full backing of the Sky board in July to continue as chairman, but there have since been more phone hacking revelations, and he also endured a revolt from News Corp shareholders last month.