Elliott's No. 9 team and Bowman's No. 48 were found in violation of a rule that covers engine assembly.
A statement from Hendrick Motorsports released Thursday said the violations were the result of an administrative error that resulted in a sealed engine assigned to Elliott's No. 9 Chevrolet being unintentionally allocated to the No. 48.
"We apologize for the mistake and have taken steps to ensure it will not be repeated," the company said.
Competition officials also deducted 25 points from each team's total in both the driver and team owner standing. Elliott's crew chief Alan Gustafson and Bowman's crew chief Greg Ives were fined $50,000 apiece.
The penalty drops Elliott from fifth to sixth in the Cup series standings. Bowman remains 11th in points.
NASCAR also issued suspensions to Hendrick Motorsports executive vice president and general manager Jeff Andrews and the organization's director of track engine support Scott Maxim for the next Cup event, at Watkins Glen on Aug. 8.