There isn't really a record kept for fewest sacks in a season by a player, as there are thousands of NFL players who have not had any sacks. Michael Strahan holds the record for most sacks in a season, at 22 1/2.
The 1988 Miami Dolphins hold that record. They managed to allow just 7 sacks in 16 games.
Reggie White set the Eagles single season record with 21 sacks in 1987.
As of the 2008 season, the NFL record for fewest sacks allowed in a season is 7 by the 1988 Miami Dolphins. The 1975 St. Louis Cardinals allowed only 7 sacks as well.
The 1984 Chicago Bears who had 72 sacks.
Texas A&M 1991 - 56 sacks
The Chicago Bears hold the NFL team record with 72 sacks in 1984.
In a non-strike season, 16 game season the NFL record for fewest sacks in a season is 13 by the 1981 Baltimore Colts. The 2008-2009 Kansas City Chiefs in 16 games I think only had 9 sacks 1988 Miami Dolphins only allowed 7.
The Minnesota Vikings record is held by Chris Doleman. He recorded 21 sacks in 1989.
Michael Strahan, N.Y. Giants, 2001: 22.5 sacks
James Harrison, 2008, 16 sacks - breaking Mike Merriweather's 1984 record of 15 sacks.