James Anderson from the UK-based investment management firm Ballie Gifford, which holds a 7.5 per cent stake in Tesla, told a German magazine that he "does not think Elon needs to be CEO".
"His micro-management also includes the desire to speak to the stock market and the world in ways we do not necessarily consider helpful," Anderson, who knows Musk personally, told Germany's Manager magazine on Thursday.
His comments referred to Musk's fondness for controversial midnight tweets that has already forced him to step down as Tesla Chairman.
Musk reached a settlement with the US Securities and Exchange Commission (SEC) over his controversial Twitter activities in April, agreeing to have more specific oversight on his tweets about the company.
According to the settlement, all tweets from Musk about Tesla's financial health, sales or delivery numbers would have to be pre-approved by a company lawyer.
The SEC sued Musk last year as well for making fraudulent statements after he tweeted in August 2018 that he had "funding secured" to take Tesla private at $420 per share.
The parties later settled and Musk agreed to step down as Chairman and have the company's lawyers pre-approve written communications, including tweets with material information about the company.
Earlier in February, the SEC again held Musk in contempt of court for allegedly violating a previous public disclosure settlement.
( With inputs from IANS )