On Thursday, CBOE Holdings and Nasdaq OMX Group said they will list options on the company on Friday.
Other U.S. options exchanges, including the International Securities Exchange Holdings' ISE and ISE Gemini, are expected to list the options soon.
The listings will allow traders to start using the contracts to place bets on where they expect the shares to trade in the future.
But given that trading volume of the stock has averaged about a million shares a day—which equates to about 10,000 options contracts—there might not be a great deal of volume, he said.
Read MoreNo one on Wall Street likes Shake Shack
The shares started trading on the New York Stock Exchange at $47 and nearly doubled to a high of $96.75 by May 22. Since then, however they have fallen significantly.
The shares ended regular trading on Thursday down 15.7 percent at $54.61, after the company said it had priced a 4 million-share offering at $60 per share, well below a $64.79 closing price on Wednesday.
"There is plenty of volatility and action, which usually attracts options traders," said J.J. Kinahan, chief strategist at TD Ameritrade in Chicago.