The recall affects only Wranglers from the 2010 model year that have automatic transmissions and were built before July 14, 2010.
The recall was announced by the National Highway Traffic Safety Administration on its website.
It says debris can get caught between a plate that protects the transmission and the catalytic converter, causing a fire. A catalytic converter is part of the exhaust system and uses heat and precious metals to control pollution.
Chrysler spokesman Eric Mayne says the recall affects about 68,000 Wranglers in the U.S., 6,000 in Canada, 1,500 in Mexico and about 11,000 in other countries.
Chrysler knows of at least 14 complaints of fires caused by the problem with 2010 Wranglers.
The company says it doesn't know of any injuries. It says debris can get trapped when the SUVs are driven off-road or through tall brush.
Chrysler, which makes the classic Wrangler and other Jeeps, will fix the problem free of charge by replacing the plate with a bar so debris doesn't get caught.
Chrysler will contact all the owners by mail. Recall work is expected to begin this month.
The NHTSA also checked Wranglers from the 2007 through 2012 model years and determined that only the 2010 models had the debris problem. Mayne said the 2010 Wranglers had a transmission plate and catalytic converter that were configured differently than the Wranglers from the other model years.
NHTSA said in documents that it had received 14 complaints of Wrangler fires from the other model years, but Mayne said there was no pattern or common cause in those fires.Suggest a correction