The Jets signed Carpenter earlier in the week to replace Billy Cundiff, who had been battling Folk since the start of training camp. Carpenter made his only field goal attempt in Thursday night's preseason finale, but it wasn't enough time to convince the Jets to make a change.
Folk has been the Jets' kicker since 2010, having outlasted annual training-camp challenges. He invited speculation about his future Aug. 24 after missing a field goal attempt in overtime against the New York Giants. Two days later, Carpenter was brought in to compete.
The Jets will open the season with Folk, but he'll be on a short leash, according to a source.
The team began to cut its roster on Friday. Aside from Carpenter, another notable release was veteran defensive tackle Antonio Garay, 33, who signed a one-year, $905,000 free-agent contract in March.