At least three people died in the accident and dozens are still missing.
Shares of Carnival's rival Royal Caribbean Cruises were down 7 percent.
Susquehanna Financial cut its rating on both the stocks to "neutral" from "positive" due to the potential impact of the tragedy on the sector.
Carnival's shares touched a near three-month low of $29.23 in morning trading on the New York Stock Exchange and those of Royal Caribbean dropped to $26.75.
(Reporting by Chris Jonathan Peters in Bangalore; Editing by Maju Samuel)