The 24-year-old, who is the son of former England striker Teddy Sheringham, has spent the majority of the past 18 months on the sidelines with a succession of injuries.
"Through no fault of his own, Charlie was very unfortunate to sustain a serious injury just a couple of months after he had moved here and he missed a lot of football," Howe told the club's official website.
"We have reluctantly decided to let him go but it was a very tough decision. We just felt that following promotion to the Championship and with the current strikers we have in the squad, Charlie was probably not going to get enough game time.
"He was a pleasure to work with during our time here and we would like to wish him all the best for the future."
Sheringham joined the club from Dartford in October 2011.