The defective part could allow the seat to fold forward during a crash.
A Tesla spokesperson told Edmunds there are no reports of a third-row seat slipping in any customer vehicle, but the company is urging owners to not let anyone ride in the third row until the vehicles are fixed.
The problem was discovered during an internal seat strength test that was conducted prior to the start of Model X deliveries in Europe, Tesla said.
Similar tests for U.S. regulators were conducted without a failure, Tesla said.
"A fix to this issue is already in place," Tesla said in a Model X customer e-mail. "We have worked with our supplier to develop a new recliner design with improved quality that resolved the issue. We are now constructing new third-row seatbacks to match all affected vehicles."
Tesla service centers will contact affected owners to schedule installment of the replacement seatbacks as soon as they are available.
"Based on current production rates, we expect all replacements to be completed on a rolling basis over the next five weeks," Tesla said. "We will accelerate this timing if possible."
Owners can contact Tesla customer service at 1-844-248-3752 or by e-mail at ServiceHelpNA@teslamotors.com.
No information about the Model X recall has been posted on the website of the National Highway Traffic Safety Administration, which oversees vehicle safety in the U.S.
Edmunds says: Tesla said it recognizes that not having the use of the third-row seats for the next few weeks is an inconvenience, but it noted: "Your safety is our primary concern." Owners should stay in touch with their service center for the latest information.