Tesla CEO Elon Musk's controversial behavior is indicative of a larger issue facing Silicon Valley, tech investor Roger McNamee told CNBC on Friday.

"The cult of founders has become a problem," the co-founder of private equity firm Elevation Partners said on "Squawk Alley."

"There's no question that great founders make great start-ups, but once a company is in the public market, once it begins to mature, it has other responsibilities," he added. "You need to have in the team people who can fulfill those responsibilities."

Elon Musk's recent tweet mocking the Securities and Exchange Commission has caused some investors to question whether founders can succeed as the CEO of a company.

In the tweet, Musk called the agency the "Shortseller Enrichment Commission," just days after settling fraud charges brought against him by the SEC. The tweet, and a subsequent note by short seller David Einhorn, caused Tesla shares to drop on Friday.