"When you talk to high-level people in the pizza industry, there are people who think this company is falling apart," Cramer said on "Squawk on the Street."
Cramer spoke as the restaurant chain's stock was 11 percent higher midmorning Thursday after Schnatter resigned as chairman of the company's board.
The departure came shortly after Schnatter admitted to using the N-word during a May conference call and apologized for the comments after Forbes magazine detailed the incident.
Papa John’s business isn't in any immediate danger, according to Cramer, because he said pizza is still a strong growth category within the food and beverage industry.
"When you see the disparity between Papa John’s and Domino's, that's share take," Cramer, the host of CNBC's "Mad Money," said Thursday.
Papa John’s did not immediately respond to CNBC's request for comment.
With a market cap of $1.7 billion, Papa John’s has seen its stock fall more than 30 percent over the past year. Meanwhile, rival Domino's has seen its shares rise nearly 31 percent same over the same period.
Cramer recalled Schnatter, who founded the company in 1984, faced backlash in November for blaming the NFL and its leadership for the company's lackluster sales. That incident led to Schnatter resigning as CEO of the company.
Cramer said investors who buy Papa John’s should "hope there is an equity offering to clean up off of [Schnatter's] stuff."