Pennock's side have secured second place in the table but are without a win in seven games.
The 45-year-old had been in charge since replacing Dave Hockaday in 2013.
Academy manager Scott Bartlett takes caretaker charge of the club, with assistant manager Jamie Day and fitness coach Neil Withington both resigning.
"It was a difficult decision just a week out from the play-offs after Ady had taken us to our highest placed finish in the National League," chairman Dale Vince said.
"However, as a club we felt we needed to make this change, in order to give us the best chance of succeeding in the play-offs.
"We thank Ady for his efforts while at the club and wish him well in the future."
Forest Green, who face Dover away on Saturday in the final game of the regular season, lost to Bristol Rovers in last season's play-offs after finishing fifth.
Promotion-chasing Forest Green Rovers have parted company with boss Ady Pennock - a week before the National League play-offs.