Chipotle was tied to E. coli, salmonella and norovirus outbreaks past year and its shares tumbled 42 percent over the last 52 weeks.
Chipotle reported its first quarterly loss ever in April, and has used a loyalty program and giveaways to lure customers back.
It's a curious play for Mr. Ackman, who has notched more misses than hits lately with a menu of souring bets.
Ackman's Pershing Square Capital Management LP has amassed a 9.9 percent stake in Chipotle Mexican Grill Inc., according to a filing with the Securities and Exchange Commission.
The announcement that Pershing Square had acquired 2.9 million shares sent Chipotle up as much as 8.7 percent to $450 in late trading.
In a public filing, Pershing described Chipotle as "undervalued" and "an attractive investment".
A stake of almost 10 percent would make Pershing Square the second-largest investor in Chipotle, according to data compiled by Bloomberg.
Arnold also said that Chipotle shouldn't franchise if it doesn't have to. But, hopefully Ackman's buy-in would restore the investor confidence and the investment firm can help the restaurant management in a turnaround. "The multiple promotions run this year have seen little apparent success and we believe a new approach may be necessary to drive a quicker pace of sales recovery", BTIG Analyst Peter Saleh wrote in a note. The billionaire investor has assumed an increasingly activist bent over the past few years, most recently stirring a shake-up at consumer-products giant Procter & Gamble that ended in the ouster of its chairman and CEO. Three directors are over 70 years old.
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Chipotle's biggest investors are mutual funds Fidelity and Vanguard and it is not widely owned by many hedge funds.
The move could reignite efforts to shake up Chipotle's nine-person board, which has been criticized for its slow response to a food-safety crisis and a lack of diverse viewpoints.
Hedgeye restaurant analyst and Chipotle short Howard Penney on Tuesday called for Chipotle's stock to fall another 50 per cent.
Bank of America Merrill Lynch analyst Joe Buckley thinks Ackman might also focus on Chipotle's generous compensation given to Ells, Moran and CFO Jack Hartung.
Morgan Stanley noted that inside ownership of Chipotle stock is still relatively low-meaning theoretically, if executive packages included a higher percentage of stock, the c-suite would be more incentivized to boost performance.
Sales at restaurants open at least 13 months fell 23.6 percent in the quarter ending June 30.
Business Insider reports Stifel analysts said they "cannot fathom Pershing's operational or mathematical investment thesis".
Mr. Ackman's past involvement in restaurant companies has revolved around financial and structural changes.