The Madison Square Garden Co. said Monday it’s considering a plan to split off its entertainment businesses from its media and sports divisions.

The New York company said it approved a plan to explore breaking into two publicly traded companies, saying the move would give shareholders the ability to more clearly evaluate each of the businesses and their prospects. The proposed separation has been under consideration since July.

The entertainment unit hosts live events at the company’s namesake Manhattan venue and at other sites including Radio City Musical Hall. The media and sports business owns teams including the New York Knicks and the New York Rangers plus regional sports networks MSG Network and MSG+.

“The [entertainment] company would capitalize on significant opportunities to grow rapidly within the changing entertainment landscape,” said Tad Smith, president and CEO of MSG. :The [sports unit] would enjoy steady growth and high cash flow that we expect will result in capital returns to shareholders.”

Madison Square Garden Co. said it did not have a timetable for the spin-off, which would be subject to final approval from its board.

The company also announced that Nelson Peltz, the CEO of Trian Fund Management, and Scott Sperling, co-president of the private-equity firm Thomas H. Lee Partners, had been nominated to its board. Peltz has recently called for PepsiCo to spin off its underperforming beverage unit.

In addition, Madison Square Garden Co.’s board authorized the repurchase of up to $500 million of the company’s stock. Its shares shot up $10.89, or 16.6 percent, to $76.67 in after-hours trading Monday.