The Rams have mustered a total of 189 points in their 12 matches this season, the second-lowest total in the NFL.
"It was, in my estimation, time to move in a different direction," Fisher told reporters. "[All of] the blame's not to fall on [Cignetti's] shoulders, but it's the way this business works.
"Players contributed, coaches contributed, everybody contributed, but we have to move in a different direction. The lack of production's obvious - we've been talking about it for weeks - and we need more production."
Rob Boras will replace Cignetti for the final four matches of the season.