James Murdoch will come under attack from shareholders at BSkyB's annual meeting on Thursday after the telecoms watchdog called his "competence" and "attitude" into question.
Mr Murdoch stepped down as BSkyB chairman amid fears that the News International phone-hacking scandal would damage the firm, but he stayed on as non-executive director.
Shareholder group Pirc (Pensions Investment Research Consultants) has urged shareholders to vote against his re-appointment due to the criticisms levelled at Mr Murdoch by communications regulator Ofcom.
Mr Murdoch is not considered to be independent as his father Rupert Murdoch is the ultimate controlling shareholder through News Corporation, the group said.
"Although Ofcom stated that the evidence available to date did not provide a reasonable basis to conclude that James Murdoch deliberately engaged in any wrongdoing, it was severely critical of him," a statement from Pirc said.
Ofcom hit out at Mr Murdoch's failure to uncover problems at News International earlier during its review of Sky's broadcasting licence in the wake of the hacking allegations.
The regulator determined that BSkyB was "fit and proper" to hold a licence but Mr Murdoch was spared no criticism in its concluding report.
Ofcom said: "We consider that the events set out above raise questions regarding James Murdoch's competence in the handling of these matters and his attitude towards the possibility of wrongdoing in the companies for which he was responsible."
As well as Pirc, investment campaigners FairPensions have called for Mr Murdoch to resign in light of Ofcom's comments.