A bankruptcy judge declined a request by Revlon Inc. minority shareholders to form an official committee to represent equity holders’ interests in the cosmetics company, which has rallied in the stock market despite its chapter 11 filing.

Judge David Jones of the U.S. Bankruptcy Court in New York ruled that minority shareholders’ interests are adequately represented in the chapter 11 case, filed in June. The shareholders’ interests align with those of unsecured creditors, who are already represented by an official committee in the bankruptcy case, the judge said.

Revlon’s stock, which has surged in recent weeks from around $2 when it filed for bankruptcy, closed at $6.80 on Wednesday.

The appointment of an official equity committee would allow the shareholder group to bill its legal and other advisory fees to Revlon. The judge said the expense of adding another set of advisers to the list of lawyers and other professionals charging fees isn’t justified.

“The unsecured creditors committee has exceptional counsel, and there is no basis to believe that unsecured creditors’ interests do not align with the minority shareholders’ interests,” Judge Jones said at Wednesday’s court hearing.

Shareholders are generally wiped out in bankruptcy cases, except for the rare instances where debt claims can be repaid with surplus of value left over. Revlon, 85% owned by billionaire Ronald Perelman, filed for bankruptcy after struggling with a heavy debt load, tough competition and an acute cash crunch.

Minority shareholders have pointed to Revlon’s surging stock price, fueled by a burst of interest from individual investors, as evidence its shares have value. Judge Jones said the chances are good that if Revlon’s unsecured creditors are paid in full, equity holders will also recover some value.

“It is exceedingly unlikely that the unsecured creditors committee’s strategy of securing full payment for unsecured creditors will result in nothing for equity holders,” he said.

Judge Jones said the minority shareholders can return to him if circumstances change to renew the request for official committee status.

The shareholders also failed to show that there is a “substantial likelihood of a meaningful recovery” for equity holders in the case. While the shareholders pointed to the substantial value of Revlon shares as evidence of potential value for equity holders in the case, the company’s debt prices point in the opposite direction, Judge Jones added.

Revlon’s 6.25% unsecured notes due in 2024 last traded at eight cents on the dollar on July 19, according to MarketAxess.

Write to Soma Biswas at soma.biswas@wsj.com