There have been no reports of accidents or injuries relating to the issue in the United States, the filings with the US National Highway Traffic Safety Administration said.
Jaguar Land Rover officials could not immediately be reached on Wednesday for comment on whether SUVs in other markets may have been affected.
The company, a unit of Tata Motors, is recalling certain 2010 to 2015 LR2 luxury compact SUVs, and 2012 and 2013 Range Rover Evoque SUVs, because a part in the occupant classification system electronic control unit may fail, disabling the passenger air bag partially or completely.
Dealers will update the restraint control module software at no cost and the recall is expected to begin on Aug. 30, according to the NHTSA documents.
Affected in the recall are about 17,066 LR2 and 23,485 Range Rover Evoque SUVs in the United States and US territories.