Earlier this year, Chipotle stopped serving pork at hundreds of locations after the company found that suppliers weren't meeting its standards.
The brand says that it will be months before carnitas are available at all locations.
Chipotle founder and CEO Steve Ells told investors there is "very little supply cushion" for pork that meets the company's standards.
The company demands that its suppliers give pigs access to the outdoors, rather than raising them in cramped pens.
Ells said that Chipotle has found a new supplier and will start replenishing the carnitas supply this summer.
If all goes according to plan, Chipotle will have a full carnitas supply in the fourth quarter.
Beef prices are also continuing to squeeze Chipotle's profit margins.
Steak and barbacoa burritos cost the company $1 more to make than alternatives like chicken or vegetarian, executives told investors during an earnings conference call.
Global droughts have led to a shortage of beef. Chipotle has started serving conventionally-raised steak in some markets to meet demand.
Consumers do eat some of that $1 cost. A steak or barbacoa burrito costs about 69 cents more in New York City. In cheaper markets like Ohio and Texas, customers pay about 40 cents more.
Chipotle executives said it could raise prices of beef items this summer if the shortage continues.
The burrito chain says that last time they raised prices on steak and barbacoa, they didn't see customers trade down to cheaper options.
The company prides itself on serving "food with integrity." This means antibiotic-free, naturally raised meats and local produce.