The Securities and Exchange Commission has opened an inquiry into Herbalife Ltd. amid an intensifying public battle between the seller of nutritional supplements and a hedge fund that argues it is a pyramid scheme, a person close to the probe said Wednesday.

The inquiry is being led by enforcement officials in the SEC's New York office, the person said. The probe won't necessarily result in any enforcement action, but it adds pressure on Herbalife a day before a meeting with investors at which the direct seller has promised a full rebuttal of the allegations lodged by hedge-fund manager William Ackman.

A spokeswoman for the SEC declined to comment. Herbalife had no immediate comment.

Mr. Ackman argued in a 300-plus slide presentation in December that Herbalife is a pyramid scheme, because its distributors earn more money recruiting other distributors than by selling products to end users. The company has said the claim is inaccurate, malicious and aimed at manipulating its stock price, charges Mr. Ackman has denied.

Mr. Ackman says his hedge fund, Pershing Square Capital Management LP, has bet more than $1 billion that Herbalife's stock will fall. He is opposed not just by the company but by others in the hedge fund community. On Wednesday, Daniel Loeb's Third Point LLC said it had taken an 8.2% stake in Herbalife, a bet that the stock will rise.

The inquiry by the SEC's enforcement division follows scrutiny of Herbalife's financial disclosures by the regulator's corporation finance division last year.

Write to Jean Eaglesham at jean.eaglesham@wsj.com

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